I'm only a backyard mechanic, my thoughts are if it runs when you give it gas, then stalls out with no gas, I'm thinking gas not electric as a problem. So many places to check:

I'd connect a hand pump line after the fuel pump, (like an out board motor hand pump) if you can draw fuel from tank through fuel pump then line is not drawing air (bad fitting at tank, clogged fuel filter, etc). If you get fuel, pump it up to carb and see if it starts.

I'd also look closely at fuel pump on motor, does it have rust in it? Was tank changed just before you bought it? (rust from old tank may be in fuel pump), maybe little valves in pump are stuck open with debris and cannot pump.

IF there is a in-line filter, I'd change it. Could be anywhere along the fuel line from tank to carb. Sometime people add the clear type you can see inside or it might be a metal style where you can't see inside.

Of course there is always the possibility you have an old rubber hose that is compromised on inside, I'd change all of the rubber hoses you find in fuel system.

sounds to me when you get gas to carb it should start.

Good luck

I wonder if you can gravity feed the carb to rule out the whole fuel delivery system.

I had lots of fuel problems including clogged filters, bad diaphragm in fuel pump, and a crack in the rubber line just after the fuel tank.

Gravity feeding the carb is possible. Disconnect the pipe from the fuel pump and securely block it, then make a short pipe that fits into the carb where the pump pipe was, connect this pipe to the alternative supply with a small outlet in the bottom that is above the carb. I dont suggest driving with this arrangement but for static use will prove a good diagnostic use and is much safer than pouring fuel into an open carb.

Tony

@anthony-williamson 

I use a lawn mower tank as a nurse tank.

If the car continues to run longer on the "nurse" tank it will almost confirm a problem in the original system. Moving the nurse tank further back along the system will show where the original system fails.

Tony

Well, I posted today that I got the car going. After 3 carb changes, ensuring all the lines were clear and no air leaks, a new fuel pump, drained and put new gas in, I found it had nothing to do with fuel. The distributor was installed (by previous owner) one cog off. I pulled it off and moved it one tooth counter clockwise put it back together and wallah!, it started and idles perfectly. No smoke, no unusual noises and it drives now pretty good. I love this car! Thanks for all the hints on possible solutions.