[pauloh]

The last paragraph below may explain the problem I've been having. The rest of this post I hope answers what Bill asked about.

Since my initial post, I have returned home, stopping two places along the way to camp. The first time I moved, I had no appearances of the "odd readout" on the Tekonsha. The last time (on my way home yesterday) the Tekonsha showed the odd readout of .10 or .20 volts when I first got under way (should be zero). In reply to Bill's suggestion, I scrolled to the "troubleshooting" menu options on the unit and saw the following information, note that brakes were NOT being applied at this time:
Battery voltage: 14.02 (to 14.04) volts
Stoplight: .04 volts (user manual seems to indicate this should be zero. My headlights/tail lights were on at this time if that could be significant.)
Output voltage .10
Input current: 0.0 amps

If I understand Bill correctly, this would indicate that no current was being supplied to the brakes at the time of the odd reading (maybe the voltage was just too low? The first time I noticed this problem it was going as high as 1.0 volts, not .10 volts) Within 10 minutes of driving, I happened to see the .10-.20 voltage reading drop to .10 and then back to the normal "0 volts" (except when braking of course), this happened in a couple of seconds as I glanced down at the display (I was not touching the unit, reference my comment in the next paragraph.)

I have noticed one more thing from reading the manual carefully. When the trailer is not connected, the Tekonsha's screen normally displays the company's logo. If the manual braking knob on the bottom of the unit is turned, the unit will start displaying "NO Trailer Connection" alternating with a picture of a trailer with a slash through it. I know I have on occasion seen this warning screen at times when the trailer was not connected, but I didn't realize its significance (I KNEW the trailer wasn't connected as I wasn't towing it, thought that was what it was telling me). I almost never use the manual control lever, and it would be nearly impossible to hit it accidentally the way I have the unit mounted, but I wonder if it is self-activating just enough to engage a tiny bit, causing the warning message when not connected, and the small voltage reading when the TM is connected. It's spring-loaded to return to the normal (off) position, and seems like goes fully back off when I actuate/release it. I'm going to leave the Tekonsha in my vehicle for a while (I usually remove it between TM travels) and keep an eye on this screen. Pressing the lever just a bit does in fact make the readout go to .10-.20 but I have to push it a fair distance before it starts to change the display. The unit is in good condition, I store it in the factory case when not in use, but maybe the switch is the culprit and needs cleaning or a factory check.