Cylinder six injector not working

Hello, did you have the resistance checked of the old #6 fuel injector checked? If the old injector had shorted out it could have burned the ECM injector driver. If you check for the fuel injector pulse at the ECM connector and it's not there, it's probably a failed ECM driver. I'll put the wiring diagram below. If you have an Automotive LED test light, you can hook it to battery positive and check for the injector pulse that way. Because the ECM driver grounds the negative side of the fuel injector to control it. And using an LED test light will draw very low current so you don't have to worry about damaging any computer components.
One other thing, if you have the old fuel injector, it should test about 12-14 Ohms of resistance. If its reading normal, try heating it up and see if the resistance drops. Fuel injectors tend to fail when they get hot. And since it's the old injector it won't matter with heating it up since you won't be using it anymore. If the heat doesn't work, throw it in freezer for a while then check the resistance, see if that makes it change. ECM drivers usually only fail because of the component they actuate. Same with Ignition coils, most coils have protection built in, but some are driven directly from the ECM and if they short out, the current flow is too much for the driver and it will burn out. Sometimes they burn out and get stuck on, causing the fuel injector to just dump fuel into the cylinder. Causing a cloud of smoke out the exhaust.

https://www.2carpros.com/articles/how-to-test-a-fuel-injector

https://www.2carpros.com/articles/how-fuel-injection-systems-work

If you have a injector control at the ECM and not at the injector harness plug, there must be a break in the wire in between the ECM and injector. Even on Ford ORM diagrams it looks like there aren't any connectors, it's a straight wire from the ECM to the injector. You may want to do a continuity check from the ECM to that injectors control wire with it unplugged and key Off. Just set your multimeter on Ohms, another thing that can cause a lack of injector pulse, and this depends on how you're testing the injector. If you're checking the injector for a pulse while it's plugged in and back probing the control wire, if there is no fuel pressure behind that one injector, for whatever reason, if something is stuck in the fuel rail and happen to end up in that particular injector output port. I've have heard of that happening before. But if you have the injector unplugged and there's still no pulse, it has to be a break in the wire.
It's not an intentional shut down or anything like that, some ECMs will shut down an injector if there is a misfire detected on that cylinder, but if you have 12 volts on the red wire and good pulse at the ECM, it has to be a wire issue. Are you getting a misfire code for cylinder #6?

You're sure the ECM pin is tight, if it's a pin fitment issue and you are back probing the ECM, you might be touching the ECM pin but the pin is not tight on the ECM connector. Pin fitment issues can be tricky, because it will test good in almost every single way, you'll have a good pulse at the ECM, you will have good continuity from the ECM to the fuel injector with the ECM connector unplugged, but if that ECM connector is not tight to the computers pin, it will throw you for a loop. If you do unplug the computer, just make sure the Key is Off. Sometimes even back probing can spread the connector female side. I use small T pins for back probing connectors.

One other thing to check if you happen to unplug the ECM connector to do a continuity check to the injector plug, see if there is continuity to Ground from the ECM wire as well. Just to be sure there is no small cut in the wire insulation and it's touches some contact point on the engine block. With the ECM unplugged and the fuel injector unplugged you should have no reading to the engine block or any ground. Just a good check to do while you're right there.

Okay, the P0356 is Ignition Coil F Primary/Secondary Circuit Malfunction. So, the Noid light pulses at the Fuel Injector harness plug? This code might be a failed Ignition Coil driver in the ECM. So, is it this code you're trying to get rid of? Is it not necessarily the fuel injector?

I understand what you're saying, are you getting a pulse at the Fuel Injector harness plug though? I know you're getting a pulse at the ECM pin for the injector. Also, since you've replaced the ignition coil and injector have you cleared the codes? I'm assuming you have and the P0356 comes back. If you have a pulse on the Noid light at the injector plug, there may be something blocking that passage for the injector. If there's no fuel pressure behind the injector, on some models it won't be able to pulse the injector. If I've got your situation correct there, I would pull the fuel rail and see if the #6 injector port is clogged by something. It seems you've covered every area multiple times.

When I have a fuel injector issue, I do an injector balance test. Put a fuel pressure gauge on the rail. Ford has a small port on the end of the rail where you can screw on a pressure gauge. Then prime the fuel system by just turning the key to on position, engine off. Get the fuel pressure up to where its max reading is. It should hold fuel pressure. Then I use a Fuel Injector Pulse tool. It powers up by the battery and has two leads that hook on to the Fuel injector. Then it has three different settings, it will pulse the injector a certain number of milliseconds. I'll put a link below to the tool. When you pulse the injector with the tool, each injector should drop the same amount of fuel pressure. For example, if it's at the max pressure of 60 PSI, when you pulse the injector, it will drop in pressure to 42 PSI, as an example. Each injector should be within 1 to2 psi of that same reading.
This is a great tool for checking injector flow. You don't need the engine on, just turn the key on to prime the fuel system. If that injector doesn't pulse, and there's no fuel pressure drop, you'll know something is blocking it in the rail.
It's strange the code you're getting, and you have spark. It might be setting that code because it's picking up a misfire. Ford has different levels of misfires. A, B, etc., depending on how bad the misfire is.
Since the ECM monitors the crankshaft speed to detect a misfire, it might not be hitting a certain criteria to set a cylinder misfire code. Cylinder misfire codes are usually set when its something that is in danger of doing damage to the Catalytic Converter. So, doing an injector balance test and pulling the fuel rail to check for an obstruction.

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There has to be a break in the wire somewhere then. Do a continuity check from the ECM connector to the injector plug. Set your meter on Ohms and check from both ends. You should have very low resistance reading. Also check from the ECM connector to engine ground. There has to be a wire corroded somewhere or broken. They do get corroded on the inside and you will find the insulation on the wire appears fine. But the inside of the wire is completely deteriorated. All it takes is a pin hole in the insulation and it will rot away on the inside. I've seen that many times. You need to track down the problem from the ECM connector towards the injector. Keep your meter hooked up to the ECM pin that controls the injector and use the other meter lead to work your way towards the injector plug. It's the only way you're going to find it. Take apart each connector along the way and look for corrosion.
Also check the Crankshaft position sensor harness plug. Since the ECM is detecting some fault, check it, because it uses the crankshaft speed to detect misfires or faults.
I would also make sure you have spark to every other coil as well. Ford is not always the best at determining which cylinder is at fault. It may be a different cylinder not firing but it's setting a #6-cylinder fault. Make sure each coil has a strong spark, Stress the coil with a larger gap and see if a coil drops out or has weak spark. You might be chasing the wrong cylinder. My Ford has done that. Was setting misfire data in Mode 6 but it was actually a loose timing chain on the other bank of the engine.