Hi, Cruiser - I have a 2010 LR4 in New Zealand, running a boat trailer with presumably some corrosion in trailer lighting circuits produced the same interesting lighting failures as you describe, when fuses (behind glove compartment blew). Cleaning up and remaking connections solved the problem, but it will happen again, so I carry a lt of spare fuses. So, my guess would be the U-Haul trailer wiring in poor condition. All my trailers have LED lighting, which causes no problems, but I put ballast on the boat trailer indicator circuits, anyway.
Of some interest, although wiring likely to be different in a US vehicle, I would certainly check out your trailer socket wiring versus US standard trailer plugs; LRs here have UK wiring glued into the rear plugs and the LR dealer who sold me the vehicle didn't know this was not NZ standard! So my electric braked trailers locked wheels immediately connection made because UK reverses pins 5 and 2, resulting in a permanent live feed to the service brakes. This was easily identified and sorted out by a local car auto-sparkey, who reversed the 2 and 5 wiring on the trailer plugs adaptor from round to our standard flat plugs (and for <10% of what the LR dealership wanted to "sort out the problem" that they ascribed to my trailers.)
