I'd suggest you check the pump relay first, but from what you've described, it doesn't sound like the problem. The way relays fail doesn't mesh with the problem you've described. If the relay didn't engage (failed open), you would have no power brakes.. its that simple.. If the relay stayed engaged (failed closed) you would have a pump running continuously even with the key off.
You stated that you have power assist and ABS. This means that: the pump runs, it charges the accumulator to its working pressure, the pump relay is engaged. The only way for the relay to close is from a signal from the pressure switch (from my memory, its a direct connect.. not through some other relay or circuit). Look at it this way: Start with the key off and pressure low, like would be if your car were parked. Now, when you switch on the key, the low pressure engages the relay which turns on the pump motor, as the pressure starts to rise, the ABS computer is signaled first (the light goes out) when the minimum pressure is reached. The pump continues to run until the 2nd pressure setting is reached and the pump shuts off.
If the ABS computer doesn't get the signal (maybe from a broken or shorted wire or faulty pressure switch) it would light the antilock light, but the brakes would function just fine and the pump would cycle as its supposed to.
So, to reaffirm, does the pump cycle on/off as its supposed to, and is the proper amount of fluid in the reservoir and which light(s) stay lit in which sequence from key on.