So I’ve had this problem recently with my 05 mustang . I’ll turn the car off and have the light switch in the off position but it continues to stay on and there’s a constant beep telling me to turn the lights off even though it’s in the off position, the lights won’t turn off , ive always replaced the **** but still nothin . Need help to fix this problem ASAP, thanks in advance !

 

What is being powered your map lights or the headlights? Your post isn't clear on which sorry.
Did you check the dimmer toggle? Maybe it's in the on position?
Im asking cause my map lights wont turn off no matter what I do. I have to pull fuse 60 or 62 from under the hood to turn them off. Have been told my sbj is no good. So I ordered a newer one.

 

. It’s not my map lights , it’s the day light running lights , like the tail lights and the side markers. They stay on as if the switch was in the on position. I can’t figure out how to turn them off

 

SJB in both cases. Inputs being ignored, there's just about only one way that happens, and that's the box it'll happen in. Probably need to look for water incursion on the right side as well, as that's usually the reason the SJBs go out. Not always, sure, but might as well look.

Well... at least from this armchair mechanic's viewpoint... might want to get a knowledgeable mechanic on that, because parts cannons can be costly...

 

Im wondering if there might be another probable cause keeping the tail lights and dash lights on. Maybe bad wiring ? Because I’ll buy the new SJB but I don’t want to have to go through the trouble of taking it in to a dealership 🙄 lots of thinking to be done sadly. I did take a look at the SJB and lots of corrosion :/

 

To address the 'other probable/possible causes' thing, without taking in the rest of your post on it...

It of course could be the headlamp switch itself, it's fused to 'on' all the time regardless of the switch position you can see/move. But if that switch isn't bad, then it's the SJB. Unless a rodent got to the wiring, or you or a previous played with the wiring and messed it up.
http://iihs.net/fsm/?d=40&f=Headlamp...olamps.pdf&p=2
http://iihs.net/fsm/?d=40&f=Turn%20S...rd%20Lamps.pdf
Notice neither the headlamp switch nor the multifunction switch directly connects to the headlamps, dash lamps, running lights, turn signals. The switchgear 'reports' to the Low Current Board, and it's 'smart'. It decides whether to turn on the lights in question, and how, and also monitors them so that it can report if any are out, which is why replacing with non-standard bulbs freaks it out and causes messages or rapid signal blink. It's also got autonomy with the lamps, meaning it can flash the parking lamps when you lock the car, for example.

If all the switchgear is in the off position, then the lights should be off. That they are not indicates the LCB in the SJB is bad, or the wiring thereto. The reason it's *likely* the SJB is because it's a known issue of water getting to the back of it in some cases, corroding the connections and/or the boards themselves in the box, and so the replacement is required at that point, because there's no fixing it... not easily anyway.

But as the rest of the post shows, there's corrosion on your SJB. Which is the wiring, to an extent, on the connectors right there. And if you see it outside, it's most likely also on the inside. The thing is toast, IMO, and yes, that'll probably be a dealership unless you get extremely lucky/do all the research and get an *exact* replacement of your current. Same body, engine, transmission and options, then you may not need reprogramming. It has reportedly been done, but there's as many 'nope, dealership' reports too.

There's a *possibility* you can maybe clean it up and repair it from the corrosion if it's not too far gone, if you're learned about electronics/wiring/dealing with circuits, but I'm not even tackling that. I'm replacing it.

Not what you wanna hear, but it's the right words, I believe. I wish ya good luck.