Wanted to update this after a bunch of troubleshooting today. Next step is to test voltage at the connector:
Voltage at the B1 fuse location is as follows:
Ignition off - 11.2V
Ignition on - 9.7V
Engine on - 10.7V
So, it looks like the voltage at the B1 fuse is low. Voltage at the B10 fuse is 12.7V, and the same at other fuse locations on the box.
What's interesting, is if I remove the B10 fuse, the voltage at the B1 fuse rises by 1V.
Now I need to determine why there's low voltage at the B1 fuse location. Problem is, I have no clue where to start!