Ballsy,
I did a job on a mates Fatboy a while back, it's about the same age as your bike. Worth a look under the rear guard. The wiring loom to the tail lights & indicators is double sided taped to the underside of the guard. Over time his wiring sagged and intermittently touched the tire, particularly two up. The insulation wore down & eventually he had shorts between the wiring which caused intermittent electrical faults. Ultimately he got run up the arse by a mate who didn't see the brake light come on as they approached an intersection.
Might be worth checking the trailer loom too. It might have rubbed or taken a nick during installation.
Pull the plugs to the rear electrics & give 'em a squirt of CRC or something similar while you're there.
My bet is it's something simple. Good luck.
Oh, and drink beer After the job's finished. ;-)
Maybe you have a mix of LED"S and bulbs???? Like bulbs on trailer and leds on bike ?? you might need a different relay ,or all led's, or fit a load inline with led's. Just guessing without all information.
A shame you weren't a bit further south Ballsy, I could have taken a look.