The reserve light should glow when you turn the key but don't start the engine, just like the rest of the "idiot" lights as part of the bulb-check procedure. The light is turned on in normal use when the float falls far enough to close a switch in the sending unit. I'd be willing to bet either that switch is full of crap keeping it "stuck" or there's a wiring issue somewhere (chaffed, poor connection, broken solder joint on the cluster, etc).

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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]