Whatever voltage the battery or the charging system is producing, less maybe a couple of tenths of a volt for losses associated with connections. There should be little or no voltage loss in the wires between connections. Dimmer switches carry a pretty heavy current, and they live in a very hostile environment where rain, dirt, and road splash is present. Contact failures inside the switch are pretty common.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!