Perhaps not "the rest of your life", but a fairly long time, or maybe not, it's hard to tell and can be fairly random. I do believe they made quite a few of them. Hopefully you didn't pay too much!
I agree, do not start on a restoration or really any work before you find the head.
While other 4-player heads *CLOSE TO THE YEAR* will certainly not match up to the wiring of Fast Draw, it may be worth looking into how close they are to others. Unfortunately due to the extremely unfortunate copyrights over Gottlieb material, this is difficult - but if you order a Fast Draw schematic (they can be bought just not easily found online) I have a few similar schematics I downloaded that we could compare to see how wide your range for searching could be, with minor adjustments in wiring needed of course.
Just shoot me a PM if you have or find a schematic for your game and I'll start comparing them for you!
ALSO: An interesting thing to note is that I believe heads are swappable so if you find a TWO-PLAYER "Quick Draw" head, it should fit if I am not mistaken. All parts that differentiate 2-player machines and 4-player machines with the same rules, artwork, and designs (carbon copy ones) are usually in the head. (Perhaps minus the relay bank relays?)
This also means you could possibly rewire two-player heads too, so it opens up the possibilities a little bit, but rewiring would work would certainly be needed, if possible/optimal at all.