Yes both trailer lights are connected to white leads on trailer harness. The white lead on pickup harness is attached to pickup frame.
Test results are in:
Fuse slot "C" in engine compartment labeled "Trailer Tow Connector" is an inactive slot so no fuse.
Fuse slot "T" in engine compartment labeled "Trailer Tow Connector" was empty so I installed a fuse.
Now getting "blinking power" at trailer connector between white and green and white and yellow pins with ignition switch on but LIGHT SWITCH OFF in the pickup. Hazards working also. No power to brown on connector which is as it should be with pickup lights off.
Haven't connected trailer yet but will do and expect all lights to be working as they should. Been working on this for almost 10 hours now with about 90 minutes out for lunch and nap. Going to have a beer now if you all don't mind.
Edit: Thanks to
herm0016 in post #29 for arousing my suspicion that a fuse was lacking even though is wasn't necessarily the fuse for 12 VDC power.
The weird thing is that I've been pulling this trailer around for about 20 years now and have checked the old trailer lights on occasion, even last week, and found them to be working without the pickup lights on.
I suspect that the new lights, being LED, may have had something to do with it since the fuse was missing. Just weird.
Thanks to all for weighing in on the thread.