OK, I watched your video. I hope you have read the work packages. You are not starting the set right. Pre-Heat is too long, and unless its really cold, not needed. You started the set with the S11, (Parallel Switch) switch on. That means you had it in the Parallel position. ALWAYS have the S11 in the single position. And leave it there unless you are going to parallel two gen set together. Have you always started the set with the S11 in the Parallel position?
Then, when you had the S1, (Start switch) in the Prime/Run position, why did you not reset the fault indicator? Next time do that and see if the light comes back on. That's important to know. If it comes back on, tell me.
You don't need to do anything to the GFI. Its not a part of your problem. In Post #1, you wrote the the 120 volt outlets have power to them. How did you know? Plug something in to it? Or use a DMM, (Multimeter). This is important to know. A DMM is the best way to measure DC voltage. Do you have and know how to use a DMM? If not you need one.
If you have 120 volts at the 120 volt outlet, then the set is producing AC voltage. You had no AC output on the AC voltage meter. That dosn't mean your set isn't making AC voltage. You need to test with a DMM.
The Frequency changed when you turned the Hertz (Frequency) knob. So this is a good sign. Do not idle this gen set. Bad things happen. If your DMM has a position to read Frequency, simply set it up, put the probes in the 120 Volt outlet and see what it reads. You can set the correct hertz, by looking at the DMM, and turning the Hertz knob. Simple.
You should also hit the Fault Indicator reset switch, while it running. See if it resets, or not. Then hold it up, and see what happens. Tell me.
The S5 (AC Circuit Interrupter) is what turns the AC voltage on and off at the load terminals. There is a light right above it. It should come on if the output contractor is CLOSED. OPEN is to turn it off.
Turn your S6, (AM-VM Switch) to the L0-L1 position.
Even without making measurements, change the switch positions and try starting the set. And hold the start switch 2 seconds longer.
OK, give it a try and let us know something. The best way is to simply click on reply and write in red the results after the question.