How to cure car cassette adapter "auto-reverse flip-flop"

Step 2 Identify trouble-maker

Ok now you can see the guts of the thing. You need to identify the bit which causes the tape-deck to try and auto-reverse. It should be a collection of a few gears which move independently on a plate. The plate swivels up and down as well. This is the trouble-maker! No one seems to know exactly why this is even in a cassette adapter which doesn't need to auto-reverse but anyway this is what's causing the problems.