Why would the brake lights stop working when the headlights are on in a 1998 izusu rodeo?

Well, the brake lights, and tail lights are different. Normally, when you turn your headlights on, your tail lights come on as well, because they are controlled by the same switch. If both your tail lights are not on, changing the lamps is the first thing to check. If both have stopped working at the same time though, it is likely going to be a wiring issue. You Brake lights, however, are controlled by a switch usually installed and activated by the brake pedal. If it has come loose or been damaged the your brake light will not light up when you brake. This is particularly dangerous. You should make these determinations and then repair before doing any further driving. Good luck!