You have to first determine weather it’s your parking lights or your brake lights, brake lights are much brighter than your parking (or tail) lights. When they’re stuck on go to front of car, look to see if the front or side lights are on as well. If they are then you have a stuck parking light issue if not and the rear red lights are only then you have a brake light issue. Either way first check that you have all the connections right on your new battery and starter and that no other wires were disturbed. If it’s ok and brake lights only then you can refine your question to brake lights stuck on. Which would probably be a brake light switch.