Have you opened up the rear hubs to see if there's any linkage for applying the brake shoes mechanically? Some 2 speeds had a habit of falling out of mesh into a false neutral situation, so hub parking brakes would be a good idea.
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!