check the earthing points arent corroded, and that it is attached to body and to ground, then check the powerline to the battery, and any other earth points straps or whatever the engine uses.

It is also likely to be alternator relay.

try wiring first as thats just time, drawing a blank then try testing to alternator relay.

my guess would be more likely a 1: corroded battery negative terminal, 2: chassis ground dodgy 3: alternator wiring and ground, 4: alternator relay, 5: fuse related to alternator.

Hope that helps