Electrical issues.

Whenever things like this happen and it doesn’t make sense, it is often a ground issue. When things are back feeding through places that would normally be grounded, it gets very confusing.

Sounds like you could be missing a dash ground. I am not familiar with a 64, but on 67-68 there are at least three different ground paths on the instrument cluster circuit board, and a ground from the metal instrument cluster frame to the dash frame.