Cusser
+1y
Yes, your running lights and instrument panel lights are from the same circuit. I'd disconnect the illumination wire for the tach first, see if that helps.
The tach illumination should draw from the little dimmer wheel switch after the rheostat.
This absolutely sounds like something to do with your new light wiring, and you did new corner lights and the tach lights, so those are the things to disconnect one-at a time. Should be straightforward.