My '98 LS had a new power steering pump installed about 4 weeks ago, I used the correct ATF III fluid. I was not too sure if I also had a leaky rack or hoses because the fluid had gotten everywhere.
I used an A-1 Cardone remanufactured pump from O'Reilly's. Same one is sold at Rockauto. I am not 100% sure my mechanic flushed the system thoroughly after the install, which I realize is important.
I do not have a loss of fluid from the reservoir, which is good, but about 2 weeks on the new pump and it started whining, and today, suddenly, I had an intermittent, complete loss of power steering. I know that on my '98 I could not see a screen in the reservoir that can be cleaned. I'm wondering if it's the reservoir screen, a bad pump, a pressure line problem or something else? I did not have wandering which would point to a bad rack. No loss of fluid in my reservoir though which I think is also worth noting.

 

could be any of the items you mentioned, or could just be that the mechanic didn't properly bleed the system and you have air in the rack or lines.

If the pump's whining, new pump could possibly be dead, though that would be pretty rare.

 

I would try bleeding it first, see if it clears it up.

When i just replaced my p/s pump on my 95, i noticed there IS a screen inside the reservoir that was very VERY dirty. when i went in to attempt to clean it, it ripped and began falling apart... what was left of it wouldn't clean up very well, and it looked like it was made of some cheap fabric/paper material. Maybe yours, if its still there, is gummed up and starving the pump?

 

My mechanic thinks the pump bearing has already failed, so flushing wouldn't help if that's true. I would like to confirm if the 98 has a serviceable screen inside the reservoir. I remember accessing the screen on my '91, but can't see it on the '98. On my '91 I also added an inline magnetic filter on the return line of the power steering pump. I think it was a great idea, I just can't find the space to put one on my '98. Crazy, my last '98 never had a single issue or leak with the power steering in all of it's 337k mile life.

 

There is a screen, yes, but is it serviceable? not really, as it is a totally sealed unit with the cap pressed onto it, and there is no way to open it up to change it. i just sprayed brake cleaner into it, flushed it with clean ATF, and made due. since it had a hole tear in it, i actually removed the remainder of the screen with a screwdriver. Alot of cars i've owned don't have any filter screens in them whatsoever, and they are fine without them

Seems like the power steering issues are common on these! My LS400 was a poster child of everything that commonly goes wrong with these when i bought it, and sure enough, it had a leaky dying pump too!