Just to make clear, the Vreg regulates the voltage difference it sees between its case and its +12 V supply wire (usually blue). Ideally, those are the same voltages as BAT- and BAT+ terminals, resp. You need to insure that is true by eliminating extraneous resistances. The factory thought a sheet-metal screw into the body was a sufficient electrical connection, and that probably worked to get thru the 3 yr warranty, but usually not true 40 yrs later.
