Were the lights working prior to the switch replacement? I'd be checking and re-checking all my wiring upgrades, fuses, etc.
As for the engine running and dying after 10-15 seconds, I would suspect a fuel delivery issue. You mentioned you changed the fuel pump. Are the hoses installed correctly, and tight. Is the hose that goes to the engine vacuum leaking perhaps, causing the fuel pump not to keep up. Those fuel pumps run on vacuum in pulses from the engine as it runs, it helps suck fuel from the tank into the carb. If it's cracked or not sealed correctly it "could" be causing you issue.
Also, the fuel shut off solenoid could be malfunctioning, preventing fuel from filling the bowl. It should open when the key is on, and close when it is off. You can test it easily by doing an online search. If wiring is incorrectly placed this "Could" cause the problem.
I am assuming it has a manual choke. Can't find a breakdown right now. Make sure everything is moving correctly.
All I got..