I have repaired cassette decks and taken apart the cassette player in these 3rd gen 4runner.
Most common issues on these stereos cant be fixed, the parts on these aren't available, ANYWHERE.
It seems like 2 companies were contracted to make them, Fujitsu Ten and Panasonic. Fujitsu Ten parts for these radios dont exist, neither do the service manuals that give you part names.
Panasonic also made these, the service manual for their radios can be found on the internet. But yet again the parts are a giant question mark. I can find some parts on Panasonic website but they are notorious for leaving stuff up long after they stopped having it.
The six CD changers that where equipped on later 4runners and early highlanders (the model not the 4runner) also frequently have issues, and you cant get parts for those either.
The model I have the most experience with is the 86120-0C020. I've taken apart 2 of them. The issue I was having was the cassette player no longer could play the tape in the other direction without buzzing. The culprit for this was a cracked plastic cog gear. Part numbers for this aren't on the internet, and there aren't spares anyway. I tried buying another stereo for parts, but this had 2 cracked cog gears so it was useless. After 20 years the plastic in every one of these stereos is at the point where it degrades whether it was used or not.
The ejection mechanism works like this. You push the cassette into a carriage, this trips a secondary motor that uses a plastic worm gear to finish pushing the cassette in. Once the cassette is in, the carriage sinks down to be level with the tape head. The worm gear then pushes the cassette to the right side of the player to engage with the tape head. The worm gear is on the left side I believe, if you spin it by hand you manually see how this process works. Mine is still in pieces sitting on a shelf next to me so I could take some photos if you like. I bet your player either has cracked plastic or a bad switch. In either case the unit is good as dead, you cant get parts. Everyone selling these on ebay as working usually only mean radio AM FM and the CD player. When I bought my parts radio the seller said everything worked, but the cassette player was fubar when I opened it up.
I might still have photos. I also chronicled this on
Tape Heads forum, the model radio I initially gave was incorrect.
I am still considering contracting someone on Alibaba to copy and make me a batch of replacement cog gears, though I have stalled sense getting the cog gear out is difficult because it is so intertwined with other components. Your worm gear is much easier to access