Since those two circuits have nothing in common with each other, I'd suspect our old friend, the bad ground. There's a group of grounds behind the instrument cluster and another behind the center console. Wonky ground connections can cause all sorts of bizarre behavior when one circuit starts back-feeding through another when it isn't supposed to.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]