Toyota Corolla CE 1999 parking lights won't turn off

Mileage on this car is 126,000, 1.4 liter engine. The parking lights on this car won't turn off, even after I turn off the engine. I've made sure the ignition switch wasn't stuck in a funky position and I've turned the lights on and off to make sure it wasn't the light switch. Before this problem developed, I noticed that the bright light indicator light on the dash board would turn on intermittently during the day even when I didn't have my lights on, let alone my brights. (The bright light indicator turning on didn't correspond to my brights being on). Turning my lights on solved the bright light indicator problem turning on unexpectedly but it seemed to develop into the more severe problem and potentially battery draining parking lights always on. (I disconnect the battery when I'm not using the car to ensure the battery doesn't drain). I noticed that there is a loud popping sound coming from under the hood, which I discovered is where the headlamp relay switch is located. I can't find the fuse for the parking lights otherwise I would just pull that and run the car with those lights.
My question: Are my brights and parking lights on the same circuit and woudl replacing this relay switch solve the problem? If not, any other suggestions for fixing the problem?