Headlamps stay on after ignition key removed and still on after 10 minutes - 2005

I have the 50th anniversary edition. About 33,000 miles now in May 24th 2021. In addition, I'm also having odd electrical issues: randomly and sporadically in no specific order: A. The Anti-Lock brake system lamp lights up signaling the Anti-lock brake system is de-activated and it actually is as I test the brakes - this is temporary - the lamp goes off after a while - still an unknown cause , B. rear wheels positive traction (limited slip) lamp goes on and off randomly on a few startup's. Note: I did have a dead battery because it would not charge after 10 years dated on the battery ! Go Motorcraft ! I installed a fresh Dealership Motorcraft battery about $100 last summer at 32500 miles. Then I had to pull both15 amp tiny passenger side kick panel fuses that run the headlights, 1 fuse each, not easy - else risking low battery or having to physically disconnect battery after each drive. I need to fix this quickly, I live in South Florida and the summer steam is coming any day now. And of course no night driving ! Any ideas ? I'm guessing something with the headlight control dial - hopefully not having to dis-assemble the entire dashboard to replace that headlight control dial. I'm thinking to bypass and install front halogen under bumper light bars so west palm police are satisfied with lights out front ? Please advise fast!
How far forward is your steering wheel? Mine was so far forward it pressed the turn signal stalk into the high beam flash position and they stayed on exactly like you describe. Didn't matter what position the light switch was in, auto or off. Won't help with your other electrical issues, but worth a check.