Why wont your 1960 falcon start?

Many things can cause this. If the care doesn't crank at all, start with your solenoid and starter. If it does crank, move on to your ignition system. Anything from a bad coil, to a worn out distributor cap, rotor, wonky timing, and bad plugs and wires. Check it all. Best to eliminate that as a problem now. If that is all functioning and set properly, check your fuel pressure. In an old car like that, if it has set around for a while, there WILL be a bunch of nasty gunk and debris in your tank. This will clog your fuel pump and lines. Clean it out and check your carb for cleanliness and proper adjustment. If your car STILL doesn't start, you may have a serious internal engine problem like low compression, worn cam lobes, bent push rods, cracked pistons, you name it.