I'm not the expert like some of these guys, BUT I think Jason, TX and Tom, Mpls are correct about the fuel problem. Here's why!
When purchased a knowledgeable guy got my 29 PU started. I then proceeded to clean & fix all the little things a green horn could do. .
Being happy took a ride and had your problems. Truck ran for awhile & die. It may or may not start. When it did go again, it wasn't for long.
Cleaning the motor compartment I noticed the gas line into the carburetor stuck out fairly far. (In my opinion ) So it was loosen up & pushed further in. I pushed it in far enough to touch the wall of the carburetor so I could only go as far as the gas in the carb. Stopping to check this or that gave enough time for gas to, not fill but leak into the carburetor. Again it start right up & only go as far as gas in the bowl of the carburetor could take me.
A few older model "A"er's found the problem. Their big joke was to see if I didn't push the tube out the tail pipe.
Hope this may be of help and yours is a simple fuel problem.