I regret taking so long to make the changes to my tail light wiring. I had expected to have it done by now, but am having a flare-up of back pain from spine surgery earlier this year. Getting under the trailer on my creeper is a little bit daunting right now.

But I will get it done and report the results as soon as possible.
Sorry, I made a mistake earlier describing my tail lamp wire
size. In several posts I said it was #14 and that is true about the molded cable on the trailer tongue. But the tow vehicle came prewired for a flat-four plug and now that I have the aftermarket 7-pin connector open, it appears that the original tail light (brown) wire is at most #16 wire. Unfortunately the size is not stamped on the wire itself, but it is definitely smaller than #14. The trailer was originally wired for 4-pin plug and used #18 gage wire throughout. The 16 tail lamps are all connected to a single #18 brown wire with a single #18 ground wire for all lamps.
I am planning to add a relay so the only load on the tail lamp wire from the tow vehicle will be the new relay coil using original tail lamp power. The tail lamps themselves will be powered by a new #12 wire to a junction box. Since the tow vehicle tail lamp wire is smaller than I thought and the trailer has the extra 80" wide lamps, I will feel better doing it this way to lighten the load on the tow vehicle tail light wire. At the same time I can upgrade the trailer wiring by dividing the tail lamps into separate groups from the junction box to the lamps on the original #18 wires.
Thank you again for all your help.
Bill
PS Dale, I appreciate the heads-up about dielectric grease and will use that on the 7-pin connector.