I had the same experience a few years ago, plus my voltage gauge dropped whenever I turned on the headlights. In addition, my headlight switch got so hot that it self destructed - melted. It was an AC Delco D1588 headlight switch. The new one had 7 posts, my old one had 8 posts, but one post had never been used, so I assume that it had previously been replaced incorrectly.
Replacing the headlight switch did not solve the voltage drop problem for me,
and it overheated too. So I then connected independent ground wires from the metal firewall to the daisy chain ground wire at the gauges. I think I added 3 ground wires. That helped the brightness and accuracy of the gauges, but the headlight switch still ran hot, although the voltage gauge didn't drop quite as much when I turned the headlights on.
So then I very carefully drilled a very small hole in a metal tab on the frame body of the headlight switch and connected a 12 gauge ground wire to it and connected that to the front metal firewall. Now the voltage gauge never moves, no matter whether the headlights are on or off, the dash gauge lights are brighter, the headlight switch does not get hot, and the interior dash lights work properly.
Jim & Kate
2016 Creekside 23RKS, 2014 Ram 1500 Eco Diesel
1995 Monaco Dynasty 36', 2005 Honda Pilot