When the ignition is turned to the on position and the dash lights come on temporarily the check engine light does not come on?

Hello, do you have communication with the engine computer (ECM)? and what scan tool are you using? The Check Engine light is an LED so it's most likely not a light issue, if a section of the ECM is not powering up the check engine light won't come on. Does the vehicle start? It's not on a fuse either, the signal comes from the ECM to the instrument cluster.
Are you noticing anything else missing on the Instrument Cluster?
Also, can you communicate with the Body Control Module?

https://www.2carpros.com/articles/how-a-car-computer-works-pcm-ecm-bcm

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Do you notice anything possibly taped over the Check Engine light? You may need a flashlight to take a real close look at the Cluster. But that light should come on at key on for at least 30 seconds.
Does that scan tool communicate with any other modules besides the ECM?

You can try to get the engine computer to set a code, try unplugging an ignition coil while the engine is running, or a fuel injector, and the ECM should set a circuit code for that component, the Check engine light should come on right away when you unplug it, then shut the truck off with it still unplugged and turn the key back on and scan it for codes,
This is the ECM circuit to the Cluster for the MIL control.

Try this 30 second delay, after shutting the truck down.

No that should have just set a code, clear the code, then turn the key off for 30 seconds, and start it up. The light should have come on with that code, there is a TSB on wiring harness damage that I will post, it's for down near the E Brake for the harness that goes up to the Cluster, but somethings not right with that light not coming on.
Do you notice anything around the Data Link Connector where you plug the scan tool in? Something tells me there is a wiring issue with this vehicle.

So, it looks like you unplugged the number 1 Ignition coil on the driver side of the engine, and the ECM is on that side of the engine compartment, so it's possible there is a wiring issue that is on that side, there is a fuse panel, the ECM and TCM located there. I would check the ECM connectors, there are 2 of them, C1 and C2, the C1 connector has all the ignition feeds. As well the MIL light wire.
Here are all the connector pinouts for the ECM.

Refresh this page, I posted the ECM connectors and pinout diagrams. Is it starting and stalling out, or just cranking over?

Okay, I'm glad it got started, but I think possibly leaning over the ECM connectors and harness may have moved some of it around, this is exactly what happens with pin fitment issues.
The starting issue sounds like the ECM lost power. We unplug coils all the time when doing a power balance test, so there's no way that would cause a no start, if you have a multimeter and test light, we can start testing some power feeds to the fuse panel and ECM.

This splice circled in red looks like one of the main GM comb splice packs where all the modules connect together to the GM class 2 serial data network. There are a couple of them in the vehicle. Check that there are no pins that are loose or that the connector hasn't been messed with.

That can be either one of the hot/cold temperature Blend doors is stuck, it can be an issue with the control module not commanding the door to move, a bad temperature sensor, wiring issue.
I think we're going to find a connector issue with the problems you're having. For example, the ECM might be turning on the Check engine light, but if the circuit to the actual LED is not complete you won't see the light,
I have been seeing a lot of connector and pin fitment issues ever since it started to get warm this year. Certain things will happen common to a lot of different vehicles when the seasons change. The fact that you were able to trigger a code and read it tells me the ECM is up and working ok, as far as we know, but you're not getting the check engine light. But we can check these things right at the ECM connector to see if the signal is making it out of the computer, and if so, then we move down the circuit to find the area where it has a bad connection. If you had a more high-end scan tool you would be able to scan the HVAC control module and there is probably a code set in there too for whatever the issue is. But you need a scan tool that can do full system scans of every module in the vehicle.

Okay, I would just check the C1 ECM connector first, since it has the Check Engine light wire in it. The connector is labelled as black, C2 is supposed to be Grey, they are not always correct on this. But you can go by wire colors too. Here's the pinouts for C1, pin 68 brown/white wire is the MIL control wire. But check all the pins, especially the ones in the 4th diagram, they have the ignition voltage, battery positive, etc. And the 5th diagram has the only Ground wire in this connector. Check for corrosion, any pins that are pushed back into the connector end, bent pins, things like that. Most of these also have a extra cover on the connector, so if you want to back probe any connectors while plugged in you will have to remove the cover. Make sure the key is off and out of the ignition. I would check that fuse panel and any Ground connections to the body while you're working in that area. If they look green or white with corrosion, they are no good. They don't put these modules and fuse boxes in the greatest places.
I think what happened yesterday when you unplugged that coil, since it was the number coil, I assume you leaned over the left hand side of the truck to unplug it? You may have pushed on some connector that is not in good shape. But see what you find with a visual inspection of all that. I will have to look up how the ECM controls the MIL light, if it grounds at pin 68 or if it sends power out to the cluster. Diagram 7, 8 are from the Cluster section and 9, 10 are from the ECM diagrams where it looks like the Cluster sends out Ignition On voltage and the ECM controls the Ground side of the circuit, but I am sure there are all kinds of connectors in between the 2.
Just don't use the Test light yet on checking the ECM, we have to be careful with it, some test lights pull too much current for specific ECM circuits. But we'll get to that. Do you know if it is an LED test light or Incandescent test light?