I just repaired a rear wiring loom for a bloke who has a Fatboy of similar vintage. It had intermittent rear brake, tail, indicator & dash issues over several months which got progressively worse. It might be worth jacking the bike up and having a good look up under the rear guard. The wiring loom is double sided taped to the guard. In his case the tape had let go towards the front of the guard allowing the wiring to drop slightly and touch the back tyre when the suspension was compressed, slowly wearing away the insulation on the wiring, severing two wires & shorting out a few more. The symptoms were similar to yours at the start but got worse as time went on.
Enjoy the ride.