Having a bit of an issue with the starting/charging system in the 64. Motor is a 250, mild upgrades.

From what I can tell of the car, the charging system (minus the battery) look to be 100% original. Car has an alternator instead of the generator, but from my searching this was the first year where alts were standard.

Before now, if the car sits for a day or two, the battery does not have enough juice to crank the motor. It clicks once or twice and requires a few turns from the start to on position before it will spin the starter. It will usually start right up at this point.

The other day after a long cruise, I parked the car in the garage and the GEN light stayed illuminated. Concerned, I looked around the engine bay for a shorting wire, but didn't find anything. I unhooked the pos battery post, and the light went off. Put it back on, and the light stays on. I unplugged the alternator (two wires leading to harness, etc) and the light goes off, but the dome light stays on. After driving it for 20 minutes to charge the battery, I parked it again and removed the pos terminal and let the car sit for a few days. Put the terminal back on and no juice for starting.

Should I start with the battery? It has a stamped date of 2006 on it. What other tests should I do to test for failed parts?