It can't be the "rebuild" of the resistor.
If you hold the resistor in this manner....
X...X....X
X.........X
The Xs being the pinouts.....then the center and top left are actually soldered together on the flex cable going into the flex resistor part. Oddly enough, the first failure mode appears to have these two connections break away from the flex cable.
Then given enough time....failure mode NUMBER 2 is to have these two connections (essentially hanging in the breez soldered together) work their way apart and now you don't have your fan working on HIGH anymore.
Having very obviously soldered this together....this means the fan should have come on....
So would someone PLEASE tell me what other fuse or fusible link is in the circuit?
Also...this means an obvious "quick fix" (provided you also don't have the "other fuse problem" I have now....is to simply jump those two connections so that your fan works on HIGH.