Bob........ I have the same problem with my 65 GS/401. Mine has the Carter 3921S carburetor. Is the carter known for this issue also?You can add a pump, any pump should serve your purpose. They should be mounted as close to the fuel tank as possible. There are kits that actually allow you to modify your tank and put them in the tank.
You don't say what year, motor, or carburetor your have, but another option is to fix the problem. The most common one with this complaint is the Rochester.
I eliminated the original choke system, installed a spacer between the exhaust manifold and exhaust pipe and opted for an electrically controlled choke. This all works just fine as it was intended to do. The rest is bone stock as it was in 1965. I don't see a valid reason to install an electric aux fuel pump other than adding another layer of trouble to hide the original problem. I do recall reading something in a GSCA article about corrosion causing the fuel to leak out but can't find it anymore. As far as being young, I'm young enough to have bought a brand new 1962 Electra 225 convertible.... lol I recall starting that motor back then and never even hearing it crank, it just started running when I turned the key. I'm going to order a rebuilding kit for the carburetor and really inspect all the components and reseat the ball in the main circuit. Thanks again for your response............ LenNo, I don't believe the Carter/Edelbrock is known for leaking it's fuel. For whatever reason I have a 2x4 425 set up which definitely does not have the problem.
Are you sure the choke is closed far enough before cranking. Also, just in case you are young and don't know, with a carburetor, you do not just climb in and crank the ignition switch. You must open the throttle a bit first to allow the choke to set, then crank. Some times a couple of shots of the gas pedal can help. You probably already know and do this, but start with the basics
So the problem could be fuel related. Looking around it seems modern fuels vaporize at lower temperatures. I always run premium grade fuels without ethanol. Maybe that makes a difference.
If the problem is vaporization, look at things like carburetor gaskets, they could make a difference. Either double or triple gasketing it, or using a carburetor heat shield.
Under-hood temperatures in general are going to effect the problem. Most header installations increase under-hood temperature.
If you eventually install an electric pump, I would choose to hook it into the ignition switch so that it only runs when the ignition switch is in the on or run position.
Here's a bit on fuel and starting: http://www.thecarburetorshop.com/Troubleshooting.htm#Hardstartcold