WAIT! Yes the TCCM is a separate device. It's basically a 'dumb' little motor driver which also lights up your dash lights. It doesn't seem to have much feedback beyond the buttons above your radio, the shifter knob position, and the transfer case motor actuator unit.
Why do you want one? Do you want one? I have an extra one in working order because I thought mine was bad. I could send it your way, in exchange for money. ($30 plus shipping? I don't really care actually) Turns out I had a different problem that I solved instead.
Is there a problem with your transfer case shifting? I've just come out of a deep-dive with this system so I'm feeling like I know it pretty well.
What noises is it making? You can listen with the engine off.
Here's how;
With the ignition in the ON position and the shifter in park you may shift between 4HI and 4LOCK.
With the ignition in the ON position and the shifter in NEUTRAL you may shift between 4HI, 4LOCK, and 4LOW.
Starting in 4HI you press the button to shift to 4LOCK, then the 4LOCK light will blink and the transfer case shifter motor will make a knocking or pulsing sound when rotating to "bump" the transfer case into 4LOCK.
If you're in 4LOCK and press the button to shift to 4HI, then the 4HI light will blink and the transfer case shifter motor will make a smooth rotational movement to shift the transfer case back into 4HI.
The transfer case shifting motor will make a smooth sound to shift into 4LO from either gear I believe, but I needed the vehicle in neutral. Otherwise the light would blink and nothing would actually happen.
You can remove the shifter motor without draining any transfer case fluid, there is a seal which prevents anything from leaking.
You can then mark its position, likely 4HI, with a sharpie or a scratch awl to keep a record where it started.
Then, you can watch it "shift" while hanging off of bottom of the vehicle. You can also test if it is rotating by touching the motor leads to a 12v jump battery and watching it turn in each direction.
Also, a simple fix might be fiddling with and jostling the shifting buttons on the dash. I hear they like to get stuck, which causes the module to throw an error up on your dash display. Once unstuck they fix themselves.
To answer your question directly though, the part numbers are as follows;
GM 24236866 is the "MODULE. Transfer Case Shift Control" which I found used on ebay for $50, and lives behind your glove box. The cover is the rounded shaped thing that is the right cover of the dash board, unacessable once the door is closed. You remove it by first removing the couple snaps on the front of it (push in the center bit, then pry them straight up and out), then popping it out the side. It's got the same snaps as the radio bezel and a bit of pressure will release it.
Here's a diagram from the manuals that Schwarttzy posted
http://schwarttzy.com/h3-hummer/ open up the manual for Hummer H3 – Transfer Case, and the TCCM is shown on page 4.
If your motor is bad, like mine was, the part number is GM 89059688, but I bought the Dorman 600-908 aftermarket replacement part, BUT be careful because the motor power leads were swapped on mine so clockwise was counter-clockwise and visa-versa which was the real headache in the whole thing for me. Once I figured that out I swapped them and it worked like a charm!
So, what is really wrong? Tell us all about it, hopefully it's an easy fix!