I recently had my clock repaired at Classic Clocks (Jeffrey Read) in Houston, TX. I absolutely could not be more pleased. Not only does the clock work but Jeffrey spent almost a week fine tuning it to keep accurate time. Right now it works amazing but over the course of time it will probably start to lose time. Typically these clocks require maintenance every 7-10 years.
Most speedometer shops want to remove the internal mechanism and replace it with a quartz movement. It’s more accurate and requires less maintenance. Such movements simply go against my grain in attempting to keep my car as original as possible. Others feel differently.
Jeffrey told me that these old VDO Kienzle clock mechanisms are essentially bullet proof and he’s never had one he couldn’t repair. As Shvegel pointed out, a resistor and capacitor almost always need to be replaced, maybe the bulb too. The winding mechanism on your clock is probably just dirty and needs cleaning and lubrication (gears, too).