Hi Peter, i have a similar problem but i also have no temp guage. Both failed at the same time. I have stripped the car down completely, trust me it is stripped. dash out and everything and i can not find the fault as yet. I will however keep you posted when i find it and find it i i will.
As for the electrics hook up foir the towball, the only place you can do it is to direct connect using scotch blocks to the rear of each of the rear lights. it is bit of a chore but it is also the only way. I have had two of these and i find it maddening to have to do this each time.
All the best
Andy
Ravenrigger