Martin -
Take a look at this diagram in my TM Tech Stuff album.
http://www.trailmanorowners.com/foru...&pictureid=442
You need to re-wire your tow vehicle's 7-pin connector to match this diagram.
The difference is that according to your description, the Jayco connector hookup has one pin dedicated to brake lights (both of them), and two other pins dedicated to left and right turn signal lights. My conclusion is that the Jayco has brake light bulbs that are separate from the turn-signal bulbs.
The TM's more standard setup does not have separate bulbs for these functions. Instead the left brake light is the same as the left turn-signal light, and the right brake light is the same as the right turn-signal light. In other words, on each side, STOP and TURN are the same bulb. This frees up a pin for the +12VDC feed (sometimes called AUX or AUX PWR) to the trailer.
To add to the confusion, each of these bulbs has a second filament inside. This second filament is used as a running light (aka marker light, aka parking light). This second filament is not related to the turn-stop function.
Bill