Bad Ground on my 67 Valiant Dash Cluster?

Which part of WV are you in? I am in western VA and may not be too far away.

MMM, yes the grounds have to be connected up for things to be working. The pulsing is normal but not with the key off. Buuuut with this last set of symptoms, I now suspect you have 12v shorted to the cluster ground. It is can be causing these symptoms by:
- When you have the key in RUN, there is 12v from the ignition switch being fed to the normal 12V input to the cluster; that puts 12v on the input of the limiter and with 12v on the ground side of the limiter due to the short, then the limiter does nothing.
- When you turn the key OFF, the 12v shorted to the cluster ground is putting 12v on the ground side of the limiter and the input of the limiter is near to ground due to other low circuits connected to the 12v ignition source 'pulling' it to ground. The limiter will then pulse; it does not care in which direction the current flows in its heating coil.

Try disconnecting/removing all of the instrument lamps and see what happens. Look at all of the nuts holding the circuti boards in place and make sure there are not washers overlapping and shorting any traces together.

Edit to add: Also remove both connectors and probe each one for 12v on each pin with the key off (with the neagtive of the meter on the chassis). There should not be 12v on any pin with the key off.