Power steering pump makes the "empty" sound all the time.

I'm getting my 1973 Duster back on the road, and among other things, there's an issue with the power steering pump. It seems to provide steering power just fine, it has nice light steering, but it always makes the sound of an empty reservoir. I've filled it, drove it around, topped it off again, drove it more, and it makes the empty sound a little when steering isn't being done, and a lot when you're turning the steering wheel.

What's wrong? Worn out pump? Or it was run low on fluid and / or with very old fluid and the seals are damaged in the pump? I've added new fluid to it but never tried to drain most of what was in there already.