It's not comms with the BCM, it's just the ignition/key start signal. 12V.
and the yellow wire is the starter relay trigger signal.. The BCM is in the middle.
Here's all I can come up with..
Ignition switch "START" -> 12V to BCM (PINK J1-14) [no power? bad ignition switch]
BCM -> 12V to Starter Motor Relay (YELLOW J4-21) [no power with GOOD ignition switch? maybe bad BCM]
Again, that 8V seems low to me.. It may not solve the problem, but I feel like you're skipping a step if you don't test those wires..
(Considering your lights all light up fine, no codes, jumping starter relay socket works, fuses good, new battery etc.)
Or find someone with a scanner that shows if the key is in the start position. (to rule out the ignition switch)