Under storage conditions like that, I'd definitely suggest a total cleanup of the starter. These starters aren't terribly complicated- - - -just a simple DC electric motor. The gear drive is mechanically actuated with the foot pedal, and the on/off switch is also mechanical- - - -just a heavy duty copper contactor that engages after the drive gear meshes with the flywheel Take the starter apart, shoeshine the commutator with a piece of non-metallic emery cloth, and make sure the brush springs have enough tension to keep the brushes tight against the armature. Replace the brushes if they're under about 3/8" long or show uneven wear. If the commutator has burned spots on individual bars, it's shorted and must be replaced. There's no good reason to go to 12 volts. A properly-maintained 6V system with a good battery will work well for a long time. Just don't have a stupid attack and put an 8V battery in it. That really creates problems! Have fun!
Jerry