On my 87 Suburban. Gregg (member on here who I bought it from) had this problem in the past when towing, it was the brake controller that was constantly causing the fuse to blow. Brake controller is now removed and I haven’t been towing anything. It’s not blown now, but from last night to tonight, the park lights in the front and rear will not work at all, but the headlights do work and the brake lights work fine when the brake is depressed.
My '86 truck does this from time to time. I found two things, a corroded fuse, and a loose connection where the large plug bolts to the firewall under the hood. I would check those quick. I even replaced the switch, before I found the real problem…