ABS light behavior

1998, 3.8l, 145K miles.
ABS light comes on when speed reaches 60 mph and doesn't go off until engine restarted.
On speeds below 60 mph - never comes on.
Brakes are working OK.
Please advise.

I had a problem with my ABS light coming on every now and then and going away on a restart. I read a post somewhere that said to top-off the fluid. I took a look at mine and it was pretty close to full, but I topped it anyway. That was about 9 months ago, and nary another light.

Thanks for reply.
I also read the message suggesting to top off the brake fluid and I did, but light is still comes on.
That's why I'm looking for another solution ,if any, besides changing a car.

you may have an out of balance tire that is causing a bad read of the ABS wheel sensor due to vibration. Perhaps it is just sutle so you need to be going quickly for it to pose a problem

There are a LOT of codes for the ABS....that will tell you if you have a problem from a wheel sensor.....and specifically what the problem is....
Then you can drill down to the problem from there.

That sounds reasonable, since my front tires are little bit out of balance.
Thank you.