The ABS light comes on when the ABS module detects a fault in the ABS system. There are dozens of component failures and open/shorts in wiring that will set the ABS light, ranging from a faulty wheel speed sensor, open/short in wheel speed sensor wiring harness, faulty hydraulic unit, fault electronic brake control module(EBCM), faulty tone ring,etc.
While it is possible the majority of the faults to be repaired at home, the fault codes can only br retreived with a diagnostic scanner with ABS capability. This has to be done first in order to know where the problem is to either repair or do further diagnostics to determine if it is a faulty part or a wiring harness issue. If the problem is in the hyrdaulic unit, this would need to be replaced by a shop as it will require bleeding afterwards with a diagnostic scanner.
I would advise spending the $50-70 to have the on-board computer read for stored ABS fault codes. Considering that most sensors cost that much themselves, you can quickly sink much more than a diagnostic fee into replacing parts based on "what usually goes out" guesses.
By your description, likely a problem in the control module, hydraulic unit, or wiring short/open. I STRONGLY encourage and suggest that you spend the money for a diagnostic scan of the abs system so that you dont spend $1200 or more on a new control module or hydraulic unit that doesnt fix the problem because it wasnt properly diagnosed first.