I assume the light comes on for two seconds when you first turn the
ignition to "II" (on), then goes off. When you turn the key to "III"
(start) and the engine fires, the light comes back on again. Correct?
Then there is an error code stored in the ABS control module.

You need to get the code read from the ABS computer. I don't know if the
engine's ECM also stores these codes or not. You can call PartSource and
see if they can read the ABS error codes for you. If not, you'll have to
get them read at the dealer, who might charge as much as $95 for the
diagnostics.

Does the ABS still work, or is it shut down? To check, find a quiet
paved road somewhere that has a gravel shoulder. At about 30mph or so,
run two wheels off onto the gravel, then brake moderately hard, with
progressively more effort. At some point, the ABS should begin to growl.
If it never does, it's shut down. I suspect it is shut down on account
of the error.

You also don't give the year of your car. There are a number of TSBs
regarding the ABS for the TL. Some are online, others are only available
at the dealer. The presence of a TSB doesn't mean you'd get a free
repair, but it may mean diagnosis might be easier.