This came from a couple of different posts from the Capri list archives (compiled from several messages):

To open it up you have to pull the black outer rim off the front and take a small brass nut off the back. The front is crimped on. If you spread the lip on the back of the front trim ring out a little it will come off and the guts will come out the front. No need to take anything on the inside apart, just blow the dust off (gently) and spray some WD-40 or a light lubricant (like tri-flow or something similar) on it.

The electric clocks in the MK I & MK II Capris work by using a solenoid to wind a spring inside the clock about once every 60 seconds. When the spring winds down it allows two electrical contacts to come together that energize the solenoid and re-wind the spring. That's about the only thing you need to look for and check inside the clock. Make sure the winder spring moves freely and the electrical contacts are clean.

Another idea if that doesn't work:

A potential easy fix for your MK1 clock! As these are difficult to find in working order, I took mine apart to see if a MK2 unit could be madeto fit into the round case, but it is too dissimilar. But, the cause ofthe problem then became obvious. The biggest challenge is getting themetal retaining ring off without butchering it, but time & patience with a small screwdriver will pry it part way around, enough to slip off. Inside, a spring loaded disk about the size of a nickel at the rear of the clock is triggered by an electrical contact, which spins it halfway around, to "wind" the clock & make the hands move. It takes a minute or two to run back to its starting place, at which the closed points wind it again. There are springy metal tabs by the coil which had become separated. I used very thin solder to resolder the connection while holding the top tab down to touch the other one. Voila! Over the past week it has run like clockwork. Definitely worth a try.