This is not an alternator issue. If the entire car goes "black" and stalls out, but you can restart it after a few minutes of resting, you have a bad MAIN battery connection somewhere, or a battery that's bad. PERIOD. I'd start checking ground straps NOW. Don't waste your time with the alternator at this point, even if it's bad, it isn't what's causing your issues.

If the battery dies, it's dead. Resting isn't going to restart the car.

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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]