The pump is a hydraulic pump, very similar (albeit smaller) than a lot of tractors, and a lot of other equipment that uses a hydraulic system.
In all of them, and I'm gonna talk about tractors since I've been involved with them for 30 years, they'll make noise IF there is (A) starvation of fluid on the suction side or (B) air introduced into the pump. Or a combination of (A) and (B). I'll call this (C)...LOL
Our cars are old. The original lines, racks, pressure hoses, tubes, they're all worn out--and OEM is becoming nonexistent unless you can find NOS, leaving us with aftermarket hoses/pipes/lines. IIRC you can still get a Motorcraft pump, and those are the only ones that are worth getting if noise is a concern. Parts store replacements will make a little noise (usually) but for a lot of us, with noisy mufflers, stereos, stock clutch fans, you won't generally hear the pump whine.
What I saw a lot of with fox body pump whine was fluid aeration. The return hose that goes on the bottom of the pump is simply clamped on both ends (pump and cooler if you have a v8 or rack if on a 4 cyl). That hose, being a low pressure clamped hose, was a source of little concern to most hobbiest-but in all actuality that hose would leak. I don't mean it would leak fluid, although in some cases it would, I mean it would allow air to get into the pump reservoir, and then the pump would pick up the aerated fluid--causing noise. That's one place.
The pump seal, can also leak-causing noise.
The noise is often amplified when the system is building pressure. This is very common and is also often seen/heard/complained of on certain tractors with HST transmissions. At rest, with no or very little pressure in the system, there is no noise-although the system is still moving fluid. Then the operator calls for a function (forward/reverse or need power assist steering) and now any noise gets amplified-drastically with an HST, not quite as bad with a Ford Hydraulic power assist steering system.
I had this issue on my 4 cylinder car. I was real picky about getting it close to OEM, in other words, quiet, smooth, etc. And, frankly I felt like I did a very good job of it--even though it was a turbo swapped car. At idle, aside from the belt there was no noise until the fans kicked on. You could hear the A/C compressor working if the A/C was on. But initially the PS pump was noisy. The more research I did on noisy pumps the more I realized that it was going to take some work to quiet it. Guy on another forum (retired Ford tech) suggested to replace ALL of the hoses, pipes, and the rack--which I had already done the rack with a 03 Cobra rack, so I also did the lines and the return hose. I forget what kind of hose and clamps I used on the return but they were not cheap junk. It was an OEM application, I think it was a return hose from a Kubota as I remember, and of course the proper clamps-which had rounded edges. Then, the retired Ford tech suggested to use a vacuum pump to "bleed" the system. I didn't believe it so I bled it the normal way, using a drill to turn the pump, and having a helper turn the steering wheel back and forth slowly with the wheels off the ground. It made a little noise. Everyone else could have lived with it, and I did for a number of months, probably closer to a year of DD'ing it. One afternoon, bored, I headed out to the shop, made up an adapter to fit into the reservoir and pulled like 10" of vacuum on the reservoir while turning the pump by hand and turning the steering shaft back and forth. Figured it was a waste of time but, nonethless, a cure for boredom and hopefully for my own OCD. Next day, got in it to head to work and noticed immediately, zero (I mean silent) power steering pump noise. At idle, there was the sound of the two belts. I hit them with some soap and the only noise was the roller followers, the timing belt, and of the alternator brushes rubbing across the rotor segments.
So yes if you want the noise gone you're going to have to work at it. It can be done, and you'll want to use a motorcraft pump as they are generally built to higher standards than parts store remans-hence why they're so expensive.
Did similar on a 3.9L V6 in a 2004 Mustang, bled it with vacuum and replaced all the hoses, it was also quiet as a church mouse. The motor was worn but the pump was quite quiet.