After New Year's I've got a shipment of brand-new turn signal switches for '62-'63 and '64-'66 coming from an original Chrysler supplier (not made-in-china copycat switches) but I don't think you wanna wait til after New Year's!
Check with Old Car Parts Northwest at 206-300-1083; talk to Ray, tell him Dan Stern sent you, and ask if he has a turn signal switch number SM-102 or SM-106. If no luck there, call up Shee-Mar at 303-678-5334 and see if they have an SM-106 in stock. The SM-106 is slightly different from your original switch in the detail of the plastic mount plate, which will have to be shaved down slightly with a box knife to fit in your steering column. Once that's done, it'll fit and work.