tom496 wrote:
I am just getting back to this problem after a few days. Thanks for the comments I received in the meantime.
When I placed a compass next to each wheel and engaged the controller, the needle turned a full 90 degrees on three of the wheels and didn't budge on the driver's side rear wheel. I inspected the wires and saw nothing suspect. I pulled the wheel and inspected the magnet and, although grimy inside the drum, there was no grease or any heavy rust anywhere.
I removed the magnet by cutting the wires. Here's what it looks like:

I performed the tests recommended here: http://www.etrailer.com/faq-testing-trailer-brake-magnets-for-proper-function.aspx using a 12v battery and multimeter. I was outside the specs:
My reading: 2.9 amps
Recommended reading: 3.2-4.0 Max amps at 12-13 volts
Resistance - my reading: 4.7 ohms
Recommended reading: 3.0-3.8 ohms
I also put my multimeter on the cut ends of the trailer-side leads to the magnet. With the controller manual lever pushed all the way to the left, I read 4.5 volts. (The reading on the Tekonsha was 6.0).
I'm not sure where to go from here and would be grateful for additional comments or advice. Is it likely that replacing that magnet will solve my problem? Does the 4.5 volt reading from the wires to the trailer suggest any additional tests that I should perform? Thanks in advance.
When you push the controller all the way with 6.0volts on controller what is the current with the one magnet disconnected?
Due to the PWD square wave output from the controller most volt meters will not be the same as what the controller reads.