You need the oil can to oil the gears.
Go to Rock Ridge and recover the missing calf for the cowgirl.
She will give you an old saddle. Swap it at the Trading Post in
Dusty Gulch (you can also swap for a gold pan, use it, and then
swap the pan for the can). Climb up inside the clock tower and oil
only the center row of gears until they are all shiny (you should
have just enough oil). Turn the crank to get the gears moving
again.