Definitely check around there.
Check on the small red one too. Can ground out inside the harness under the engine/timing belt front cover.

That small red wire comes from a multi-wire plug at firewall. You can run a new dedicated wire from firewall to back of alt. You can do the same for the oil sender, I think.

Unfortunately the '84 is in the years of the self-destructing wire harness: insulation crumbles. So rewiring is often done.
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Sven: '89 245 NA, 951 ECU, open-front airbox, E-fan, 205/65-15's, IPD sways, E-Codes, amber front corner reflectors. Wifemobile '89 245 NA stock. 90 244 NA spare, runs.