I have a 1995 sc300 with similar symptoms.
It stopped starting one day (machine gun like clicking).
I reaplced the battery, it worked again.
Now (2 months later), when I open/close windows, flick the wipers, or draw electical current the engine may shut off and the ABS light may come on.
I have the 2JZ engine and am not sure of the PS pump location, but do you think there may be a bigger problem? I really can't afford to have alot of work done on the car to debug some phantom electical problem...