OK, I managed to rig up a small harness for testing. I discovered the connectors are manufactured by TE Connectivity and was able to locate the correct part directly from them, bypassing the dealer. A little freeze spray and +13.8V later and I've isolated the problem component:
Video identifying the problemI'm unable to identify the QFP component in question though, so if anyone has insight that would be helpful. I'm attaching a higher-resolution image of the board, but it has these markings:
D (company logo?)
457789-0723
F016A9007
0721 Z02
I don't have much experience in this area, but I haven't come up with anything while searching. There are a few Chinese suppliers that list "457789" or "D457789" chips and their use by Toyota, but without any further details or datasheets. There have been a few references to NEC, which would make sense as a Japanese manufacturer, but nothing concrete. If it is something bespoke just for Toyota, is it likely that the chip is failing internally, or is it more likely to be bad solder joints? Is it possible that getting this component re-worked would be enough?
I'm also getting some coil whine (audible in the video) from a large transformer on the power supply board that I'm also unable to identify. It's marked:
P13
K7327
Obviously schematics would be the way to go, but given that these are boards internal to Toyota and were only replaced as part of the larger assembly, that's out of the question.