John, your engine was made on 13 October 1981. I think that was somewhere near the time Briggs and Stratton changed from the large one-piece flo-jet carburetor to the two-piece flo-jet, so it might have either.
I suggest you begin by looking at the cap on the fuel tank, and ensuring that it is the original Briggs one with a vent to allow air into the tank. Your symptoms are a good match for having a sealed (non-vented) fuel tank. Next, if the fuel tank cap is the correct one, turn off the fuel tap, disconnect the fuel line where it attaches to the carburetor, put a cup or clean tin under the free end of the fuel line, and turn on the fuel tap. See how fast fuel flows out of the fuel line into the tin. If it is a decent full stream that continues without slowing or stopping, you don't have a blockage in the tank or line.
Next step is to check the flow rate into the carburetor float bowl. You will need to reattach the fuel line, turn off the fuel, remove the float bowl (if you have a one-piece flo-jet), put the tin underneath the carburetor, and turn the fuel back on. Once again, observe whether you get a full flow of fuel into the cup, or a slow, more or less dribbling flow. If you have a two-piece flo-jet, you will need to remove the main jet, which screws into the left side of the carburetor at a 45 degree angle underneath, to make this check - if you are in doubt, post a picture of the carburetor and we can take it from there.
Please post the outcome of these tests.