Finally all put back together. I can't explain the wacky behavior (like how the lights would work just by touching the fuse but not installing it) but it's functioning properly now. I'm thinking the fuse spot for the red wire was indeed a spare at one point in time. There's a suspicious surface-mounted conduit that runs along the shower ceiling and houses the red wire. First, the red wire isn't consistent with the rest of the rig's black/white wiring scheme. Second, all other wires run through the ceiling. The wire exits the conduit up into the ceiling and into the roof vent. This is the wire that was feeding the shorted out circuit. I added another wire to the conduit to bypass the shorted wire.
I'm thinking there has been trouble in the past with this circuit. Counting the "spare" fuse, there are 2 fuses feeding the circuit. There's a second one labeled "LIGHTS" that when removed causes the lights to go out. So who knows? With that dead short on one path, it was somehow back feeding enough juice to dimly light up the lights.
Not how I wanted to spend my morning but I'm glad it's fixed.