I believe the 91 does not have variable assist power steering (VAP). So in that way you have the simpler system. And yes, the pump would make a noise all the time if it were the culprit. Is your new pump new enough to be for the VAP system? You have a directional control valve in the system, and the hydraulic fluid makes a noise as it is forced into a small passage to run the rack one way or the other, but it is usually a muffled howl. Sometimes check valves will chatter and make a chainsaw type noise, but that sound doesn't fully describe it.
Did the old pump have crap in the fluid when you emptied it out (like solids)?
Try a flush (you can search it on this forum) and if you can, try to do a reverse flush if that is possible. That would free up any solids that made their way to the valving and is partially restricting the orifice.
Before that step, try some true "Type F" tranny fluid, in case that will make a difference.