I have that same factory head unit. I installed it in the supercharged car. Everything worked, but it needs to be dismantled and cleaned up, or possibly repaired, as the EQ is VERY touchy on the slider knobs, and the radio either gets quieter, or there's a cracking/popping when you adjust them. I think the volume knob also has that issue, IIRC. Probably an easy fix, but yet another project I don't have time to delve into right now. Someday... Currently, I have aftermarket stereos in the other 2 cars, and if it aint broke, don't fix it! The car I just bought has a brand new head unit, so I'll replace all the blown speakers, and leave it in there until I can work on the factory radio and EQ. That'll buy me the time I need.
Side note: The antenna actually works on the new Celica. My '82 didn't but the PO also replaced the windshield with the internal antenna, so no big deal there. The supercharged car antenna worked when I got it, but only for a few months, and finding a good replacement from junkyards, proved futile, As did replacing the mast with a factory Toyota replacement, so I broke down and went aftermarket, eventually.