High idle?

Hello, are you sure you're not dealing with either a large vacuum leak, or the idle air control (IAC) valve being stuck open? There is a TPS on the throttle body, and the IAC, but from service info, the cruise control module is what you're seeing on the actual gas pedal itself. It has a rod which pulls the on the throttle cable in this system and that's how the PCM controls vehicle speeds. If you are looking at throttle plates with the vehicle running, are they staying open too far? Keeping the idle that high. I'll post the cruise control operations here for you, but you do see a throttle cable going to the throttle body, correct? It's not a drive by wire system, with that much carbon build up, I would suspect the idle air control valve to be carboned up as well, it would take a pretty huge vacuum leak to keep the idle at 2500 RPMs, or it could be a combination of things.
I don't see a MAF sensor, so you could take a look at the throttle plates with the air intake tube off the throttle body and it shouldn't affect engine running at all. But the IAC is bolted to the throttle body, so I would take that off and see if the valve is stuck open. A bad PCV valve will cause this much carbon build up as well. Let me grab some service info for you.

The first two diagrams below are the Cruise Control operation and the module that is on the gas pedal, diagrams 3,4,5,6 are for the Idle Air Control valve, this type of IAC valve doesn't control the throttle plate movement, it just allows air past the throttle plates via a port on the side, and they do fail, but I would also check the intake manifold gasket for any vacuum leaks or any cracked vacuum lines/hoses that you see, if you have the intake air boot off and the throttle plates are staying closed while its running, which they should be, then inspect the IAC and other possible vacuum leaks into the engine, the EGR port going into the intake manifold tend to get carbon build up as well, not just the EGR valve. It might be setting a code because the PCM is looking for a change in manifold pressure when the EGR valve is activated and it's not seeing the correct reading from the MAP sensor.
The guides below will help as well, usually when checking for vacuum leaks we would use a smoke machine, but you can try using a spray bottle of water and spray around the intake manifold gasket area and listen for it drawing the water in, it's a pretty noticeable sound with a large leak.
Now if the throttle plates are staying open at idle, due to the cruise control pulling on the throttle cable, you will see the plates open, and the throttle cable will be tight. Thats how this system works, the cruise control module pulls on the throttle linkage, and that's how the PCM holds the RPM and vehicle speed.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

https://www.2carpros.com/articles/engine-idles-too-high

https://www.2carpros.com/articles/idle-air-control-valve-service

https://www.2carpros.com/articles/how-a-idle-air-control-valve-works

If you can take a picture of the larger hose off the intake and post it here, that would help ID it. I suspect that might be possibly the brake booster hose. As for the P0121 code it wasn't listed in the service info for some reason. But a search for it states TPS A Circuit Range/Performance Problem, which could be caused by the sticking throttle body, but testing the TPS sensor on the TB is pretty easy, if its 3 wire, then it's going to have a 5volt reference feed from the PCM, a signal wire back to the PCM and a Ground.

So, if you're going to test it by back probing its connector, have the key on, with a multimeter find out which wire is the 5 volts, (ill post a diagram for you), and which is the ground wire. And just to verify the sensor's circuit integrity back to the PCM, use the sensor's ground when checking the 5volts. Then leave your black meter lead in the Ground and probe the signal wire, and the voltage should fluctuate roughly 0-5volts as you move the throttle plates by hand.
I will post some further testing info here for you in a minute, just to simply things.
But with so much carbon build up you could be dealing with more than one problem.

You may or may not see the plunger move on Key On engine Off, depending on when the PCM moves it, if there is "false air" coming in due to a large vacuum leak, during cranking and starting the air/fuel mixture is already going to be messed up. But yes I would check that as well. If the throttle body was that bad, the IAC will have carbon build up too.
But during a cold start up, the vehicle will be in Open Loop operations as for the fuel system status, so it will mostly be looking at the coolant temp to control idle until it warms up enough,
Here is the wiring for the TPS on the throttle body, the Grey wire is the 5volt feed, the Black wire is its Ground through the PCM, and the dark blue wire is the Signal which should fluctuate with movement of the throttle plates, just set the meter on DC volts, when back probing the connector use small probing pins if you have some, or T pins (diagram 2), just probe directly in next to the wire, don't force anything, but just enough until you feel the connector pin and get a reading, if the 5 volts is missing, unplug the sensor and recheck using battery negative as Ground.
I will look for a vacuum hose diagram, although I didn't see one yesterday when looking.
Also, what are all the codes you are getting? And can your scan tool read live engine data?

Okay, so there are 2 different designs for the throttle body and vacuum assembly for this vehicle, the first is diagrams 1, 2. With the throttle body facing sideways, and the vacuum hose routing in the diagram 2. Diagrams 3, 4 are for the Secondary AIR Injection system, which might be what you were questioning. Its purpose is to add oxygen into the system to light off the Catalytic Converter faster and get emissions under control quicker.
Diagrams 5, 6 is the 2nd Throttle Body and vacuum design, still uses the same components, located pretty much the same way, just that throttle body facing upwards, TPS and IAC located same place. Evap canister purge valve located the same place.

If the IAC is stuck retracted, therefore allowing the idle air port to be open fully, you may not see it moving at key on if it has carbon built up inside it. Don't pull it out though, its ruined once it physically pulled out like that, but on live scan tool data, there should be a data PID for IAC counts or position. If there's a wiring issue to the IAC, and it's fully retracted, see if unplugging it has any effect.

Since this isn't a drive by wire setup where the PCM would be controlling the throttle plates by itself, the TPS is just inputting throttle position to calculate fuel injection, the high idle has to be air getting into the intake by some means, that's what you're really chasing here.
The AIR injection system is going to pump air into the exhaust during cold start up, but it does have some vacuum related components, the vacuum line running over the valve cover to the Combination valve.

But I think this might be more of a huge leak such as the intake gasket or IAC, just being that the idle is so high. Something to consider is that the PCM right now is not trying to control the idle, or can't, with most vacuum leaks on this type of design the PCM would be opening and closing the IAC in an attempt to bring the idle down and under control, but it's not doing that all it sounds. You would hear an idle hunting type of reaction, so if the leak is big enough, the PCM would just close the IAC altogether.

There is a procedure when replacing this IAC, the pintle needs to be retracted using a scan tool, (this is per service info), and there is an idle relearn I will post here.

Okay, refresh this page, I posted more service info. I will put up the service info on replacing the IAC, they want it retracted with a scan tool before installation, then a quick relearn procedure you can do with just raising the rpm a few times.
Was the IAC stuck retracted?

Okay, well just try not to push the pintle in by hand, I haven't done one of this style in a long time, but I don't remember retracting it with a scan tool either to be honest. So just follow the install info as best you can, and do the RPM relearn, I think you should be ok. They are a cheap part, the last issue I had like this on an older vehicle turned out to be the intake gasket, but that car had some control over the idle, the PCM would accelerate and slow down the vehicle by itself while driving, but our service writer pulled the pintle out by hand and ruined the IAC that was current, so we had to install a new one anyway. But looking back, the PCM did have some control of the idle speed. And it was exactly this same setup.

You too, thanks, let us know what you find.

Does it feel like the gas pedal itself is pulled down during this time? Some of these codes are still pointing to false air getting in, vs a sensor reading incorrectly and the PCM causing this, such as a bad engine coolant temp sensor reading very low temp can cause an older vehicle like this to have a high idle, but you have a very high idle, plus we're seeing some of these Secondary Air injection codes pop up. Along with the P0037 which is the rear 02 sensor reading a lean (low voltage condition). The rear 02 will read roughly 0.1volts to 0.9volts, low being lean, and 0.9v being rich air/fuel ratio.
And the p0507 high idle speed.

I think the EGR codes are just because manifold pressure is probably all over the place and the PCM cant get a good self test run on it,
The diagrams below 1-4 are for the P0410 code, Air injection, you might try clamping off or blocking off one or more of the larger air pump hoses or even just regular vacuum hoses off and see if it happens to bring the idle down or effect it in any way,

There has to be a large source of air getting into the engine, or the PCM is causing the IAC to open up for some reason, what happens if you unplug the IAC before turning the key On, and then starting the engine, you might have to feather the gas pedal a bit to get it started but does that have any effect on the idle?

The P0507 info is diagrams 5, 6, 7.

But try unplugging the IAC before key On, and if that doesnt help, try blocking off the Air injection pump hoses with the EGR unplugged for now,

Something else that just came to mind, is the Air Injection system pumps air into the exhaust during cold start up, but the EGR also allows exhaust gases back into the intake manifold under heavy engine loads to lower cylinder temps, so if you think about it, we could have a case here where the Air pump is pushing air into the exhaust and this being an electronic EGR valve, might be just allowing that air right back into the intake manifold.
It sounds crazy, but almost anything is possible when it comes to automotive diags, Ive seen stuff that cant always be logically explained, although I was want it to be,

So you might even just delete the EGR valve temporarily by blocking off the valve completely until we start to get this figured out.
All this will set more codes, but thats ok we need to find out where this air is coming from. Its going to be one of these systems setting a code, of course its probably staring us right in the face, but the last diagram shows the Air pump and its hoses.

I remember another truck doing something crazy with the idle, right after starting up, the IAC would just slowly open itself up for no reason, and we found the PCM unbolted flopping around behind the glove box, it had been damaged because of smashing around in there. It was another weird situation, there was no other obvious issues at all, it just went from very low idle to high right after start up. But that wasn't setting any codes either.
Just to be sure, take a look at the Engine coolant temp reading if possible, although I don't think that's our issue here.

Okay, just try some of those things when you get back, have a nice vacation in the meantime.