Most likely, there is a crack in one of the drive wheels on the cassette player. I have seen this in pretty much every old toyota deck I have pulled. The4 drive wheels crack, a tooth or two falls off, drive wheels get jammed, deck thinks the tape needs to be flipped. You can search the interweb to see if you can buy new wheels. If you want a cassette deck and have it look stock, look for the newer double din deck out of a toyota. I am not sure of the number, but it was normally found in 97-2001 Camry, Avalons and Tundras. You can usually find them on ebay for cheap too. Mkae sure that it is the internal amplified one(two connecters on the back, not one) Part number is 86120-0C020 or 0C030. The only thing you will need to do is swap your harness to the newer one.
1976 RA29 project car, now a driver!!!!!
1985 MX72 soon to be...