my guess is that the jiggling of the wire had nothing to do with the starting. I'd bet on your starter (unless you have replaced it recently), that it is in the early phases of failure. Clean all the connections, including the fuses (turn them a couple times even if they look intact, they get corroded at the ends sometimes) and see if you still have problems. If you do, replace or rebuild the starter.

Peter
1985 300TD

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Peter
1985 300TD 4-speed 212K
1992 400E 343K
2001 E320 72K