These Rover clocks have two contacts inside, one fixed and one which gets closer to the first one as the mainspring inside winds down (as the clock ticks). As they touch, it energises a coil which winds the clock up, and the process starts again. The commonest cause of failure is either the contacts becoming pitted (as there is a tiny spark as they contact) in a similar way to contact points, or the coil burning out, which means of course that the clock will not wind.
The contacts can be cleaned carefully with emery paper if you dismantle the clock after removing it from the dashboard, but a burnt out coil pretty final.
It may be possible to have it repaired, but on a 30 year old unit, you might not be able get the spares!
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