a loose connector will draw extra power. it acts like a resistor the connector will heat up and eventually melt. prior to melting down, it will draw more and more power as time goes on. you have to check the ground wires too.

could be electric fuel pump connections, alt connections, coil, dist, ecu, etc.

you need to check all of them remove the tarnish (grab your girlfriends emery fingernail board or some sandpaper) clean all the connectors up. fix any loosies. with it running you can maybe find what connectors are heating up. they wont zap you except for the coil & plug wires (ouch)

the main culprits are usually wires that run close to headers. neutral safety switch, etc.