Ran into this issue last year, it’s the stalk switch. Full current runs through the stalk, and over time the contacts get charred. Disassembly is easy and there are many good threads on here detailing the procedure. Clean the crud off the contacts and you will be good to go.

 

Add an appropriately sized diode in line before the stall and it should never happen again, or at least take a lot longer.

 

What about installing 99-02 headlights in an 04?

 

I certainly wouldn't advise switching to facelift front lights, they look good, that's all. They fog up as they age, the lens discolours and they also get stolen, why, who knows.