traction control and abs lights stay on

usually a speed sensor, there is one for each wheel, front hub bearings are very common on those cars, and for the front, the speed sensor is part of the hub bearing. Usually with a speed sensor cruise control will also fail to work, it could also be a blown fuse, or abs modual (quite expensive)

usually, with a bad speed sensor, the light will not come on untill the car starts moving a few mph, where as with a fuse or module the light will come on right after the car starts, it needs to be scanned though to figure out what the code is.

I just had these 2 dash lights come on together, had a complete brake job 2 weeks ago and a water pump today, now i have this issue it seems to be driving perfect, wht could this be/

Abs light with the traction control light just came on when i started the car cadillac 99 sts seville what is the issue drives fine

ABS pump & possibly modulator valve need to be replaced. Car will drive fine but without the ABS and Traction Control functions (traction control uses the ABS system to modulate braking on a wheel that is spinning so it slows down and grips). Expensive to have done (about $1500) but if you want to keep the car, its worth it. Just had it done a year ago on my '93 Coupe deVille. Pumps are getting scarce for mine. Not sure about a '99.