I agree with CABLE
So ( If memory serves ) the TIP of the speedo cable is NYLON on one end.. ( and I'm thinking the speedo side) the ends get rounded and no spinny.
If I'm thinking of a later model, the problem is the cable gets rusted and binds and the actual cable snaps internally.
So try the following,
Jack the car up.....PROPERLY
Put car in neutral
Crawl under there.
Disconnect the speedo cable.
Have assistant turn rear wheels
Watch tang( where the cable hooks into ) in tail shaft to see if it spins..
Inspect cable...
I think you can pull the entire cable out via the bottom...
re lube it ( if it looks OK)
I like to use WATERPROOF boat trailer bearing grease..it's a BLUE MESS to work with... but it does a GREAT job for this kinda stuff!
Slip it back in..
Now the mating part at the back of the speedo SHOULD be a square and NOT rounded out make sure that when you get it back in you turn it as your slipping it back and it should jump back into the hole.. up behind the dash..... have your assistant open the door and watch the speedo... you spin the cable down there...
Does it work... are you spinning the right direction?
the other thing...is I forget if the speedo sleeve ( on back of speedo) is a spring retainer or a threaded deal... make sure it's seated as well ( not disconnected)
Good luck!
Vig!