I have my '57 Starfire 98 convertible in process of a mechanical restoration and had the clock rebuilt with a quartz movement. When it came back to the restorer, the case was larger than the original and wouldn't fit in the dash. My only option for quartz was to lose my second hand on the clock. I opted to go back to the original style movement to keep the second hand.

 

A little over a year ago I posted this, this was my solution after facing the same problem, I had a donor clock sitting on my shelf un used
Just a cheap Chinese desk clock, ( quartz movements are available at just about any hobby shop Hobby Lobby ETC..)
the winder in the clock was crispy critters and I was considering sending it out for conversion when the cheap *** in me said hey maybe I can fix this. In my 56 super 88 there are only two screws holding the clock in, it takes about 1 minute to get it out, so I removed it took the back housing off and removed the works, I had to slightly enlarge the hole in the face I installed the movement (after painting the hands)
the housing fit over the movement allowing me to retain the factory illumination and there you have it. Yes I will have to replace the battery about every year and a half but like I said it's only 2 screws and about a minute of my time. maybe this will work for you, good luck !!