Been there and I feel your pain.
In general, trailer lighting connectors and wiring aren't built to a usefully high standard and fail often and for no reason. If it's any consolation, the boat trailer guys have it worse.
I offer herewith Jammer's version of the Shining Path to Trailer Light Happiness:
1) Find and remove any and all insulation-displacement connectors (you know, those blue scotchlock things) on both the trailer and the tow vehicle. Replace them with soldered connections sealed with the high-buck heat shrink that has a layer of hot melt glue inside the tube to encapsulate the connection and protect it from water and salt spray. This is the most important step
2) Find and remove any and all butt connections and terminals that do not show clear evidence of being crimped with a proper ratchet crimp tool
. Either replace them with properly crimped terminals or solder them.
3) Be sure that any wiring exposed to road debris or passing through or across a metal component is protected by wire loom
, conduit, or a grommet. Better still, use loom over all the wires everywhere.
4) Avoid relying on grounds to the steel frame of either the TV or the TT, use a wired return instead. If unavoidable, crimp (using the ratchet tool) or solder the wire to a ring terminal of the proper size and fasten it to the frame after sanding or grinding the frame until bright and shiny. Use a stainless steel star washer between the ring terminal and the frame unless you can find some ring terminals that have the star washer built in (they're hard to find)
5) Aggressively replace any connectors and bulbholders that show any sign of corrosion or damage whatsoever, unless they're rare or expensive or impossible to get at.
6) Use anticorrosive electrical grease on bulbs and connections. The stuff the home centers sell for aluminum wire works great and is readily available.
7) Consider that the 6-pin and 7-pin connectors work better than the 7-blade RV connectors because they have a better design and larger contact area. The 4-way/5-way flat ones are the worst.
8) I think it's usually worth wiring a relay and circuit breaker for the trailer running lights rather than just wiring them to the tail light circuit. With 16 marker lights and two tail lights that circuit draws considerable current, and there are ample opportunities for them to short out leaving you to wonder what happened.
9) The relay and circuit breaker approach works with turn signals too and although usually unnecessary it is one way to solve the problem of fuses blowing when you go over a bump once in 5 hours of driving.
Probably not much help if you're on the road Friday, I guess.