If you want to keep it original, there is a set of contacts that often will not make contact and kick the spring back. You can see if it runs if you pull the spring back by hand and if so, use some emery cloth and clean these contacts, it may start working.

 

Get yourself a copy of Hemmings classic collector car magazine. They used to offer one free copy if you request one from the internet. Anyway, there are a few companies listed in the Mustang parts section that offer clock kits. Years ago I bought a kit for my 70 Mach 1. They even sent a "how to video" with the kit. It was easy to replace the original clock works with the modern quartz movement. From the outside you have no idea that the inner workings have been changed. BTW, the clock works perfectly now. Of course in a 70 Mach 1 the driver can only tell the time between the hours of 2:15 and 6:15. LOL, the veiwing angle leaves a lot to be desired. I think the company I bought my clock kit from was in Illinois. "Specialty Instruments" or something close to that was the companies name. I paid about $60, back in 2000 or so. Again, it was extremely simple to make the swap. I highly recommend the change.

 

Car clocks were notorious pieces of crap back in teh days of yore. It didn't matter which manufacturer, you were lucky if the thing worked for a year. Often it was oxidized contacts. A pencil eraser works to clean them and is less abrasive than emery cloth. To change to a quartz movement is a great idea.

 

I can scan and post the instructions if anyone wants them.