Depending on the environment the clock is in, WD40 may not be the best idea to leave in place; the stuff can gum up. Its probably fine for cleaning and freeing up the mechanism.
A long ago article I read recommended using a strong solvent/degreaser (1,1,1 trichloroethane) which is no longer available followed by naptha (lighter fluid), or just naptha but it would take more time and work. Both need to be kept far away from any painted areas. The naptha would reportedly provide a little bit of lubricant left behind as the rest evaporated
I cleaned my non-rally clock (which was frozen) mechanism with Berryman B12 carb cleaner (the good stuff before it got EPA'd), and lubed it with micro-Kroil on a toothpick, and it has been working for years now in my garage. Wish it was working in the car!