The single wire from the solenoid is not a ground wire. When 12v is applied to that wire, such as from your backup lites, it energizes the solenoid and prevents the trailer brakes from working so that you can back up now. But, you must have been going forward before putting into reverse to allow the trailer hitch to extend in order to relieve any trailer braking pressure.
Also you can't back up an incline, put truck in forward to reposition and then back into reverse, won't work. You would have to block the trailer wheels and roll truck forward to extend trailer tongue 1st, then back into reverse for your final position.
Tie Down sells a very nice solenoid that will relieve all pressure in trailer that eleminates this design flaw of the standard back up solenoids.