At the very least, you need to replace the calipers on the brake for that wheel.
Even if the brake is not binding sufficiently to cause a "pull", it is binding sufficiently to overheat the brakes on that wheel.
An overheated brake mechanism may also mean that you need to replace the rotor, and--of course--you want to see just how badly-worn the brake pads are. Also, make sure that you flush the brake system and refill it with new brake fluid of the correct specification.
After doing all of the above-noted work, if the symptoms persist, then you may need to replace the flexible brake lines. Brake lines can deteriorate on their inner surfaces after many years, and since your car is now at least 14 years old, the flexible brake lines may well be in need of replacement.
The only thing about your post that find confusing is the reference to a "brake-on light from that wheel".
I have never seen a brake warning light specifically for one wheel.