Chris
Hopefully you have at least one inch of space behind the clock face. There is one method of lighting signs I developed back in 2005 on my HO modular layout. It uses the same technology as backlit signs on commercial buildings. It will do a clock face as well.
Since it is a clock with a round face, you need a round plastic styrene tube of the same size as the face. Plug one end with a round piece of sheet styrene. Drill 3mm holes in the end. The 3mm leds will be glued into these holes or hole. The layout of the holes will be so the leds are at least 1/2’’ apart. The led(s) will be lighting the inside of the tube.
Once the leds are glued in place, fill the tube with clear silicone caulking. The caulk acts as a light diffusing material. It will also act as a glue of the clock face. The caulk dries overnight.
The clock face is made on your home computer with your preferred drawing program. You then print the image on clear overhead transparency material. To seal the ink permanently to the transparency, use Testor’s DullCoat. Cut the image & set it on the end of the tube into the caulk.
Your building will have a hole cut into the side of the wall where you want to glue the tube into place.
Since you are working with leds and it is an illumination project, test as you go so that you have the desired effect & your electrical is a ok once complete.
Use black paint to hide any light coming through the wrong places.