remove the panels that cover around the ignition and either cut the wire that feeds power to the light or cut the wire and add in a switch and shut it off. but really the best way would be to actually find out whats causing it, probably a wire shorting to ground somewhere but since its nothing super important just cut or add in a switch would be the best fast way.
the green light is used too see the ignition. but in your case its used to light the vehicle......lol sorry
you might have to cycle to key 3 time and on the third start it. put your e-brake on and put the truck in neutral. this is the standard dodge ecu reset. if the problem persists. you will have to take the fuse out. or trip the circuit.