A very brief search and it seems like the control module for cooled/heated seats is the same for 2007-2013, can't imagine they would relocate it just before discontinuing the truck, but i've been wrong before just ask my wife =).. Can you share a picture under the front of the passenger seat just to confirm?
Second, if you get a scanner capable of reading body codes (not just check engine 'P' codes) it may tell you exactly what is wrong with the heating/cooling module and/or the thermoelectric blowers. I have my eye on the Autel AP200 Diaglink after the recommendation from a fellow forum member. It is the absolute cheapest scan tool that will read B codes, you have to go mechanic level tools and spend $2k+ for most tools to read body codes.
Another thought, search for 2012+ escalade and yukon denali CCSM locations, they were identical (or close to it). This will help cast a bigger net, as there were not near as many sales of the 2012-2013 Avalanche as compared to the other high-end model GM SUV's. Even the top model Chevy/GMC pickups will likely be similar.