I'm not familiar with Hot Air cars too much, but electricity still works the same no matter what . How do the connections look at the back of the Alt (the car has a hot-wired pump right?) If those connections look good I would look at the relay thats triggering the fuel pump. Over time with most of these relays controlling the power side, they tend to spark when the relay is engaged. After how many cycles the contacts wear out. The relay can still "click" but it wont supply power to the component. Make sure the wires and connections are in good condition and change the relay out, and report back.
Prime Wire !
First unplug the prime wire that is located wnder the master cylender !
On the side that goes to the relay, hot wire it !
Run the engine and reinstall the wire from the relay back onto the
prime under the master cylinder !