I went out today prepared to go through things based on all the advice here. I started by inspecting the 7-pin plug, and with the brakes still not working, decided I'd pin out each connection in the plug to its associated wire to test that the actual 7-pin connector plug and cable were OK.
When I opened the junction box to get access to the other end of the cord, I found the blue wire for my brakes hanging by a thread, pretty much disconnected from the marrette, which would explain why the brake controller is reading "no trailer brake".
Poor craftsmanship (provided that it is original). The wires that are connected via marrette were only stripped back about an 8th of an inch, and were barely joined inside the marrette. I stripped them all back and reconnected (and taped them), and voila, everything works again.
I'll likely replace the marrettes in the JB with crimped connections in the spring, but I've solved my problem and can put her away for the winter with peace of mind.
Thanks for all of your suggestions.
2015 Ram 3500 Laramie Crew Cummins Diesel
2013 Jay Flight 26BH