If just the brake and tail lights are doing this then it's most likely that ground wire. Dirty starter issues usually manifest themselves in freaky turn signal behavior.
One caveat on rear Run-N-Lites: Filament bulbs left on constantly generate heat. K bike lenses are not designed for that and rear Run-N-Lites will, over a long span of time, gradually warp the lenses a bit. I've seen it on several bikes that I've parted out that had them.
Lite-Buddies are better IMO.
And a 56011 Lite-Blazer license plate frame is even better than that.
(http://smithduck.home.comcast.net/~smithduck/bmw/k1100rs/pics/licframe.jpg)