The final driven gear for the dial does not line up completely with the mating drive gear.
One of the gears determines the cycle time and is interchangeable. There is a screw to loosen, then the plate with the mating gear can move. Tip: a 50% mess will work, if they are too close together they could jam.
I'm wondering what is the best way to clean up all the contacts and help protect them from excessive wear?
If they are really crusty, knock the chunks off with a dental pick. Very light on some emery cloth is all that's needed. The fingers ride on the bakelite cams and don't wear much. The cams determine which lights are on during each interval. The dial keys determine how long each interval will be.
When you have things apart you will see where to oil. Light motor oil, don't over oil, the excess will drip out, collect dirt and gum up. These motors are low torque, slow speed.
I haven't got mine yet, should be soon. Then I'll have photos to go with the words.
One thing you will need is the 15 pin connector, eBay $14. I'll be getting a wiring diagram put together as soon as I something to look at.