The White Gnat's manual odometer will keep "rolling" with the key off, but when I was driving the Jimmy, it's odometer (fully digital, apparently) would stop recording. So I would do the trick of turning the key back on right after the engine died. But this probably caused my lights to flash, etc, so I didn't like to do it at night, especially.
I'm now starting to experience trouble with my starter switch on the Gnat, so probably the fuel injector kill switch AND a start button will be the "ticket". Gotta get on that before I find myself unable to turn the starter in the middle of the night somewhere!!!