Hi, this is my first post here and to be honest I registered just to be able to post this so that this might help anyone else who is having the same problem I had.
I had no tow bar at all on my E61 and I badly need one, so I decided to retrofit the swiveling one.
After installing and coding everything ($3AC option) the button still wouldn't light up and there would be a communication error present on the AHM module. After double checking every single pin and verifying they indeed match up to the TIS diagram I felt there must be something obvious I am missing.
After digging through forums and literally any even remotely related information on the web for 3 days it turns out the solution was at the same place as the problem. Here's the short and long of it:
TIS has two types of diagrams - one for the AHM 3+ module and one for the AHM 4R. I am using the latter (4R), so I took the corresponding diagram and followed it precisely. Turns out the pin 7 (AHM_ALIV) is wrong in the diagram! It should be the pin 11! And I randomly stumbled upon this in TIS itself, there is a page describing how one would upgrade from AHM 3/3+ to a 4R and it says that wire from pin 7 must be moved to pin 11 in the connector. Every single other wire on the diagram matches, but this was the head scratcher that took 3 days of guessing.
I hope this at least saves some time for anyone having this problem as I was starting to question my own sanity by the end

 

It gets like that sometimes and it sucks that you have to figure out a TIS doc that should be straight forward. Sadly, there's a lot of those instances in TIS. Glad you were able to figure it out.

 

This is the first time TIS has lied to me and I have done loads of retrofits and fixes in the past. Well, trust is broken now