Thanks Uber. Great post. I'll pull it apart again and take a look behind the head unit to see if I can find another lead back there somewhere.
I just spoke to the previous owner (DeclanM3 on the forum) and he mentioned that to his knowledge, the head unit is original and that it used to work prior to having a bluetooth install.
I've opened up the C Pillar and all the connections to the amp appear to be fine.