On the M939A2 getting to the PCU to check solenoids, power, etc.. is the hardest part if it's a winch truck the cover is kind of a PITA. The bench test for the solenoids (there are only three) is easy and cleaning the valve block is easy. The CTIS manual has pinouts for all this if you can use a meter you can track it down. Start with power supply, check solenoids, check pressure transducer, check pressure switch on wet tank.
You may also want to check the hub seals. There's a tool for that in the TM you can easily make your own. I made mine out of a gas pressure test gauge from the hardware store and then swapped the gauge (for a 100psi one) and added a 3/4" JIC male fitting. You unplug the flex line from the hub to the frame, plug in the tool and inflate. If the hub seal is bad you'll hear it. If you take the tool off and it deflates the tire then the QRV on the wheel is bad. This will eliminate that variable which is huge. Be advised that, at least on my M936A2, the army used SAE fitting for the front wheels and JIC for the rear wheels (yes I checked the -24P). You do you but I wanted them all the same so swapped them to JIC all around. I keep my test tool on the truck and the cap for it is also the plug for a flex line. So if I blow one on the road I can run with 5/6 wheels on CTIS and hand manage the last one.
This is important: get a shop air supply of 120psi setup and run the truck off that. You can't hear anything and work on the system with the truck running. This is huge. Seriously. Do this first.
Another great thing to do is download the "P2P" program on this site and get it to run. You may have to goof a bit on your computer to get it to run in "compatibility mode". It's really super helpful the animation of how the CTIS system works is great. This, the CTIS manual I posted a page of above, and the Army TM for the CTIS system is all you really need. It's all available on this site.
My latest project, an M1078A0, has a non functioning system with a blinking terrain all the time. Turns out the pressure transducer in the PCU was bad and it was just waiting for it blinking all the time. So a new one from Amazon for like $20 and it started working. It promptly deflated all the tires until flat every time it checked couldn't stop it once started. I definitely have a blown hub seal......