That is odd you get a different result from a different voltage reg.
is it the back up VR solid state as well or the old style?

Can you measure the output of the vr with and without the lights on? see if it is cutting out?

It isn't the sending unit, so it must be the dash.

Can you add a ground directly from the battery to the frame? or even the cluster. The bolts that hold it to the frame should be the ground.

If that solves it, then it is just bad grounds. I would see if the column got insulated some how and isn't grounding as expected.