Electrical issue 94 GC 3.3

Hi guys, was hoping for some advice, searched around on the forums but didn't find anything...

My battery mysteriously died last night, about 1/2 hr before I had driven it a short distance, shut it off, when I came back, it was dead.

Got a jump but it would not idle. Left it on the cables for 10 minutes while other vehicle was running, no idle, instantly died when foot was off the gas. Had it towed home.

After it was off the tow truck I took out the battery and stuck it on the charger overnight, put it back on the van this morning, same thing, would start and instantly die. Held it running for a couple minutes but just wanted to die.

Came inside for about an hour and searched around online, decided I needed to check the charging voltage so took out the voltmeter hooked it up across the terminals and started the van up,

the van ran great. Didn't die, Idled fine. Charging voltage was moving around between 13 - 13.5 volts so I think the alternator may be fine....

I'm going to clean out the throttle body, get some throttle body cleaner and do that asap. Anything else I should look for? Should I just do the alternator anyway or stick a new battery in there? Alternator is original.

Thanks a lot for any help!!