Code 412???

Is the IAC plugged in?

If so, has it been cleaned recently?

For general knowledge, the IAC is the Idle Air Controller. Below is a picture and a write-up on cleaning it. Note that IMHO one should NOT clean the IAC unless prepared to replace it. Sometimes they crap out after being cleaned. However, if someone looks inside the thing and it looks like a chimney, there's not much choice.

Ford Mustang IAC IAB - Solving your idle problems

It's nice when we can help the newer guys out.

IIRC, that write-up doesn't mention a lack-of-idling-when-cold as an IAC issue, but it is. You're older like me - the IAC performs part of the function of a choke.
It also increases the idle for the AC and it performs a dashpot function (another carb term lost on the kids).

FWIW, I like to use WD40 instead of carb cleaner. I fill the thing up with WD and let it marinate for about 15 mins. Then rinse and repeat. It takes several times to get it clean. Then on the last round, I use a quality cotton swab (you don't want cotton lint stuck inside there) to 'swab' out the guts. You'll get a lot more crap out of it. Then I rinse it once more (no soaking) with electrical contact cleaner and put it back in.