I have an SC400, not SC300, so don't take this as gospel, but....
Power steering pumps can last a long time, but on our cars many of them had seals that died prematurely, causing them to leak. I lived with the leak for a long time, but eventually, it started to make loud, turbine-like noises that varied with the engine speed and I replaced it.
Under normal conditions, power steering pumps and water pumps last long enough so that they are not part of any service procedure at any mileage, but when you change the timing belt, you may as well change the water pump. A lot of the same stuff must be removed to replace either part and you sure don't wanna go thru (or pay for) that procedure any more often than you have to.
There's a lot of debate on this, but I think 60K or even 80K is way too early to replace the water pump or the belt, at least on the SC400. Plenty of other opinions on all of this is available on other threads if you wish to search.
The noise you here is common from the belts. That sound is probably your power steering pump drive belt.. Pulleys rarely go bad with the pumps. What usually happens with the pumps is that they will leak after a time, but there is no set interval for replacing them. There are rebuild kits for the pumps and when perfoming side jobs I will use that, but at the dealerships we don't rebuild, we replace. My suggestion for you is to replace the drive belt and that should take care of your squeaking noise.