On my 84 380SE which had same problems,

The ABS light was ixed with a new OVP relay.

The battery was also draining fast (4-7 days and it won't start) simply becuase of it's old age as it won't hold charge, which probably was made worse because it was not used frequently.

Before I got a new battery, once or twice during low battery power situations, (ie engine just barely started) the ABS light did come on intermittently, which seems to correspond to the previous posts where ABS systems needs a certain voltage to work(?).