2001 Toyota Corolla AC question

Hi, I’m hoping someone can help me out. My kids inherited a 2001 Toyota Corolla from their great grandma. I’ve been tending to some “deferred maintenance” to get the car running in tip top shape. I thought I was done until I got a P0505 idle air control DTC. Since I’m a student of Matt I didn’t fire the parts canon and diagnosed the issue properly. 12v feed, 5v reference, ground and I even checked for waveform. All looked good so I replaced the IAC after cleaning and reinstalling the old one just in case it was just gunked up. CEL went out immediately and I thought I was done. But as I’m bringing the engine up to temp so I can refill the coolant I noticed the AC clutch is engaging intermittently even though the it’s 35F here in Chicago and the AC is turned off. Not the off/on off/on off/on like a loose wire is rattling around. But rather it engages for a few seconds and then disengages for a minute or two. Then it cycles again. It drops the RPM from idle of about 1020 to 620. It does this in park, neutral and drive. I know the AC system is low or completely discharged because I drove it home in late fall and got no cold air. So after my lengthy diatribe my question is, should the AC clutch be randomly engaging when turned off and should I be looking at an electrical or possibly a driver issue? Thanks in advance, Chris.