There are 4 nuts holding the assembly in place. Also remove two general lights and the high beam light (all are typical 50s GM light sockets). Then carefully remove the glass trim piece (usually it will be crimped in three or four places). Set the trim piece, glass and rubber piece aside safely. The needle must (emphasize must) be removed carefully. I think you said yours fell off. That is pretty rare and might indicate another problem. Usually the needle hub is bonded to the shaft fast. Then there will be 2 screws holding on the face plate. Please do not lose those. They are not a common size. Two more screws hold the movement in the case and there will be a rubber piece for sound deadening. Or there should be. Once you get it removed, please let us know what you find. Occasionally lack of lubrication will cause problems but rarely does it create the sort of action you described. I have some images (including how to refresh odometer numerals). First we need to see what is happening.
