Rebuilding a carburetor can be a daunting task if you've never done it before. There are tons of small parts, screws and gaskets that need replacing, and a lot of pieces that need cleaning or ...
Confirm that the fuel valve is on, there’s gas in the tank and the spark plug is in good shape. Shoot a one-second burst of aerosol lubricant or carburetor cleaner down the throat of the carburetor.
The carburetor sitting on your vintage Mustang can be a finicky device. It has minute passages that air and fuel travel through to feed the engine the fuel it demands based on load, rpm, and so forth.