Many thanks to Hafrod
I did the same thing with my '56 clock.
I thought I'd post some more pictures in case anyone else wants to make this mod. The more pictures the better for me.
Took the old clock apart and cut the back off of it using a Dremel and a cutoff wheel.
Marked off the areas to remove to allow the square clockworks to fit into the round clock.
I cut some rubber spacers, about an 1/8th thick and enlarged the hole in the original clock face backing.
The spacers are inserted between the old clock back face and the new clock
in order to adjust it to the front of the clock face and the hands.
Mounted the new clock works in the housing and cut the new hands down to size.
I got some model airplane paint and painted the hands too.
My new clock was different than Hafrod's, it had a spot to mount an AA battery built in,
but I stuffed the green LED (12V, RadioShack) under there and extended the LED wires
and the battery contacts out with wires too.
I got 12V from the original lamp socket wire for the LED (so it would dim)
and connected a ground wire to sheet metal.
I connected a AA battery mount from RadioShack and mounted it in the glove box.
Hooked up the wires and reinstalled the clock and speaker grill and it all works great.
Clock keeps perfect time and the light in the clock dims and brightens with the rest of the dash lights.
And as you can see, I was all done by 2:00 O'Clock.