My power steering pump on my 73 screams when at full lock. It also will do it the odd time before full lock if the car is hardly moving. It seems to me its when the pump is loaded up. Fluid level is correct Lines appear to be tight...I guess suction could be still be leaking but... Car has had less than 3000 miles since restoration 10ish years ago so I can't see that the fluid needs to be changed. What is the likely cause of the pump screaming? Do I need to change the pump?
Listen to CorkyE. When the belt slips, it screeches. The pump likely isn't capable of making a screech. Put on a new belt and adjust it right. Then after driving it for a few days, readjust the tension. That has solved every screeching power steering system I've ever worked on.
Mine did the same thing. When I installed VA on my 73, I decided to freshen up the pulleys. Sandblasted, epoxied, painted them satin black. I painted in the grooves where the belts go. Big mistake. Ruined all the new belts. Paint got impregnated in the belts and they screamed just like you are describing. At random my PS would get hard to turn and squeal. Thought it would wear off but didn't. It ruined the new belts. May be something to look into.
Have had PS pumps make a noise when they start to go out, however, more like a moan and groan , then a squeal
Here's kind of how I look at it. Belts are cheap and I'm not going to put a new pump on with an old belt, just me. So, buy a belt first and if that's not the problem, you have a new belt to go with your soon to be new pump. IMHO