After about 20 years of age my OEM radio's rewind function started to act funky. Pressing rewind caused the tape to auto-reverse instead.
Other rewind-related functions (like skip track, repeat, etc.) acted similar with unexpected auto-reversing. Fast forward seemed to work fine, though.

The issue can be puzzling but the reason is rather trivial: Over time the capstan belt of the tape drive wears out. Due to the layout of the mechanics the reverse movement is affected more strongly than forward or fast forward. To make it short: The belt needs to be replaced.

After removal of the centre console and the climate control unit the radio can be removed from the chassis by opening two screws on the top and two at the bottom. Now detach all connectors and it's a breeze to take it out.

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Next we are going to open the top of the radio housing by unbolting tow screws on the top and two on the back.
Note that the metal is locked into the front plastic so lift it up starting at the back and detach it from the front as the last step.

The cassette unit is attached to the chassis by four screws. Two on the front (which hold an additional metal guide) and two on the back.

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After removing them the unit can be simply pulled up and taken out.

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To replace the belt, turn over the cassette unit and locate the two screws that hold the bottom metal plate.

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After removing the two screws, lift the plate up slightly (don't damage the ribbon cable) and slide it a few millimeters towards the top.
This releases the two bottom taps holding the plate in place and when it's moving freely it's simply pulled out away from the ribbon cable.

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A suitable replacement belt has a length of ~408 mm equivalent to a diameter of 130 mm. It's a square cut belt with a height of >1.0 mm (probably 1.2 - 1.5).
It can be sourced from CSI Elektronik in a 1.0 mm version that works fine but the same length at a height of 1.2 would be even better.
Note that the worn-out belt had a diameter of 135 mm. 5-10 % is a typical figure for wear up to the point of failure (thanks, goldnsx).

Nevertheless, be sure to avoid any twisting when installing the new belt (which can be a little tricky) and we are back on the road enjoying our favourite 90s mix-tape and rejoicing on the CD-like track-skip and repeat feature