I also applaud this young man for getting involved in this project. I just retired a couple of years ago as a lead mechanic from the local transit company near Seattle. I can definitely say that techs of all kinds are becoming very rare. Keep up the good work! Mechanical aptitude is defined as "a measure of a technical or engineering candidate’s mechanical reasoning and mechanical comprehension to succeed in their domain. It implies possessing a theoretical and practical knowledge of mechanics and mechanical associations." In simple terms to me this just means the desire to figure out how things work and then repair them. That will be your best asset as you progress. Don't lose it!
At 60 I decided to retire early. I still liked what I did at work but the politics of working for this "blue county" where I live became more than I could stand. I won't go down that rabbit hole, but I can tell you that I actively "play" up in my shop. Over the past few years, I've bought 23-24 different MEP surplus military generators to play with. These are amazing machines and I've come to appreciate them greatly. I've also come to really appreciate this forum in the process. The willingness of all of these people to give their time freely to help others is simply amazing! I've also tried to give back when I can.
I've recently rebuilt (2) different 4L80E's for "LS swap" projects. I'm using the stock P59 PCM's out of the "doner vehicles" to run the 6.0L engines as well as the transmissions in both of these projects. It can seem like a daunting task to trouble-shoot something electrical when it's not working correctly. But, as others here have already mentioned, follow the trouble-shooting trees accurately and don't leave any steps out. I must add here that I'm not familiar with the HMMWV's. So, I do not know how the 4L80E transmission is interfaced electrically with these vehicles? It sounds like a separate PCM?
But because you haven't actually seen this transmission in this vehicle work correctly, I would start with some fluid basics first before diving into the electrical abyss. Drain the fluid, replace the filter and refill the transmission to the proper level with the correct fluid. There's also a test port on the left side of the transmission case. (Get yourself an ATSG manual for this transmission...they're about $35 and full of great information...also the TM's here on this forum are something that you'll want to familiarize yourself with) If you have access to 0-300 PSI gauge, thread it into the transmission and see what kind of pressure you have. You should see 40-70 PSI at idle and 160-180 PSI with 2500 RPM or more. I know that this unit is supposedly "new", but none the less if you don't have any fluid pressure then there's no sense in throwing more time at trouble-shooting the electrical components when there's an internal problem with the pump.
Good luck, and have fun in the process!