The part which bolts to the engine is pretty common and should be pretty easy to find. You can start with a classified ad in the classifieds section of the forum.
I can't speak specifically about a '60 but on '61-'64, the 6 cylinder mounts directly to a cross member which is just behind the radiator. Since the V8 is shorter, the V8 trucks have a bracket which is riveted to the frame. This bracket will be the hard one to get because you will need to find someone who is parting out a V8 truck and is willing to remove it for you. Another alternative is to have a bracket made and welded in place.
So first, make sure a '60 is the same way so you're not looking for something that does not exist, and then try to find or make one.
Lawrenceville, GA