Alternator meter is jumping around and the lights are dimmed... won't stay running

But if no body ground things will ground through any path.

There might be one by distributer to firewall. Or as noted earlier. From battery negitave to rad core support.

I agree the engine running then died. If the engine was running too slow the ammeter would bounce and lights could be dim.

I would check for grounds AND get the engine running reliably before worring about the ammeter bounce