A bunch of issues

So I got a 85 Nissan 300zx. The lights on the car at night, ALL of them will pulsate as the car runs. What should I do? When I first got the car the battery in it was dead and had enough juice to jump it but it wouldn't start after that. I swapped the battery with another car of mine and it starts fine. But at night the lights pulsate.

Hey mate,

Have you got a multi meter you can test the out put of the alternator with?

Sounds like it's gone kaput.

Sounds like a bad diode is letting some AC current through the alternator. Both of my 85s did that at some point. The alternators on the Z31s are pretty weak (around 60 amps).

Well we had to jump it to get it off the truck. Once it was started I drove it around the block home and turned it off and tried to start it again and it wouldn't start. So i took the battery out of my 91 corolla being its top post also and tried it. The car started. The battery in my corolla is like maybe 600cca. I wasn't sure if the battery from it wasn't strong enough to keep the 300 running and that was why the car lights all pulsate. If it was the alternator wouldn't the car eventually die? I drove it a little today. A good 20 minutes or so and it never died. And I know the battery in my corolla is good cause its my daily driver. Any thoughts?