My car's ABS light is on

Sounds like you have two possible issues. The brake pulse sounds like warped rotors assuming this happens when you press the pedal? If so, then you need brakes and that will most likely take care of the check brake system light as well because that normally means the brake fluid is low.

https://www.2carpros.com/articles/how-to-replace-front-brake-pads-and-rotors-fwd

However this will not cause the ABS light to come on and if the pulsing is not just when the brakes are pressed then we may have a wheel speed sensor issue or some other ABS issue.

Which means we need to check the codes first and foremost. Here is a video that will help with this:

https://www.youtube.com/watch?v=rTtAnsOlZU4

Let's start with this and go from there because once we know what codes are there we can figure the next steps. Thanks