Will I just be able to replace the caliper and finish the rear brakes or do I need a new ABS module?

Hi! this is Bo with Car Genius! I assume you weren't driving the car. If that's the case, I'd install the brake pad, bleed the system to get air bubbles out and see if that warning light goes off. You may have to replace that caliper and if the parking brake shoes are contaminated with brake fluid you'll have to replace those as well. If you have any other questions feel free to give us a call at (877) 913-1554