The reply by CorsairDeluxe covers this well, about what you can do if you change to 12V, to make it work with the Kaiser "designed for 6V" system. Here is a reply from a very knowledgeable Studebaker and other makes guy Gord Richmond--one of those real 'go to' people. So, a voltage reducer just won't work on a 6V solenoid if you change to 12V
"Jim, this comes up again and again. The problem with the overdrive solenoid is that it has two modes of operation, pull-in, and hold-in. The pull-in coil is wound with relatively few turns of heavy wire, and sucks a lot of juice for the brief period of time that it is working to draw the slug through the bore of the solenoid. Once the slug slams home, overdrive is engaged, and a disc on the slug hits a contact leaf and opens the circuit to the pull-in coil, leaving the hold-in coil, which is wound with many turns of finer wire, still energized.
At a guess, the solenoid might draw 20 amps for the half-second or so that it takes to pull in, and 5 amps for as long as it remains engaged. I have never measured it. A voltage dropping resistor that is sized right for the hold-in coil won't pass enough juice for the pull-in coil, and conversely, one that is sized right for the pull-in coil would pass too much juice for the hold-in coil, and it might eventually overheat and burn out.
What you would need is a solid-state regulated voltage reducer, with enough capacity to supply the 20 (or whatever) amps required by the pull-in coil. This would likely cost more than simply buying a 12-volt solenoid.
If you were really determined to do things the hard way, you could open up the solenoid, find an end of each winding, detach it from its terminal, snake a lead through a hole in the case, and equip each winding with its own independent voltage-dropping resistor. (and then snake the other lead from each resistor back into the case and solder it to the appropriate terminal) "