What type of fluid for a 69 convertible top pump?

You might find that repeated use will work the small air pockets out and foam will dissipate. You might find that any type oil will foam a little as it returns to the reservoir where a air pocket is.
I wouldn't run it up and down repeatedly for extended period as that would only agitate and increase foam and just might over heat something too. It wasn't designed for yoyo operation.
Compare to filling a power steering system. Fill it, run it briefly and let it sit still while foam disappears from that reservoir, then check level, repeat. Eventually the foam is no more.
Used to. Now a vacuum pump is needed. Twice in a month i have come across this. Had a gmc van that got a new pump. Steering would shudder. Removed all the “power steering” fluid and replaced with atf. Noticeable and instantaneous difference. Atf is one of the best hydraulic fluids you can buy.