I'd like to thank CBODY67 for saving me a lot of typing, because he covered a lot of what I was going to say.
I have a '65, but as far as I can tell the instrument clusters are the same.
The Factory Service Manual should have pretty detailed instructions on removing the cluster from the dash. It is not difficult, but it is fiddly. If you don't have the FSM, you can download it here.
Service Manuals – MyMopar
Two things to emphasize when pulling the cluster.
1. Disconnect the battery. You will be working with the 2 wires to the ammeter and don't want big sparks under the dash!
2. If you have a column shift, disconnect the link that goes to the indicator needle, or you will break that linkage.
Once the cluster is out, you remove the machine screws around the outside of the front and that releases the black and clear plastic cover. (don't miss the one down in the deep hole in the middle bottom)
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The lower gauges are attached with more machine screws.
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Now turn the cluster over and unscrew the 2 screws above and below where the speedometer cable goes. That will release the speedometer mechanism and its metal faceplate from the housing.
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Once you are that far in, it shouldn't be too hard to figure out what's binding up. In my experience if one of the odometers jams up it will just chew up the plastic gears, but anything is possible.
You can chuck that short piece of cable in a power drill and run it in reverse to bench test things.
While you have it apart, this is a good time to clean and test all the light sockets and touch up the orange paint on the needles if needed. Definitely clean the connections for the ammeter. When I just did mine, I actually put double nuts on the studs holding the meter to the circuit board, and then 2 more nuts to hold each of the wires on. Any bad connection there leads to heat, and that's when your ammeter melts the dash.