So I recently purchased a second '64 98, and a previous owner had hooked up an electronic fuel pump back at the gas tank. The problem is, they ran the power straight to the battery connection, so whenever it hooked up it is running. My question is, where do I need to hook it up properly so that it is only running when it needs to be? Any advice would be appreciated. Thanks in advance!

 

The previous owner of my car did the same thing - strait to the battery.
They ran the negative wire to the bracket that held the pump and then tie-wrapped the bracket and pump to the fuel lines up at the tank.
Makes me wonder what he was smokin'...

Th3e IGN1 circuit would be the best place to use - same circuit as the coil, backup lights and trans. Depending on the pump, you might need a relay.
If you have a good stock factory mech fuel pump, the electric one really isn't needed.

 

The original pump is still there, it's just been bypassed. I hear that unleaded gas eats up the diaphram though. Do they make rebuild kits with newer materials that can handle our cruddy gas?

 

You could also consider putting a switch under the dash to shut the fuel off as a security measure...

 

Any new fuel pump will be made to handle unleaded gas. The ethenol crap may not be that good for it or any other rubber seals. The risk to both types of pumps are victims of it.
The fuel pumps are not rebuildable, so just buy a new one.
Use it and ditch the electric. Airtex makes a decent pump for little cash. If you are not running a super modified engine, the mech one will serve you just fine.