Trying to restore some old tools. I've done a reasonable job of stripping the paint, and removed all the rust with vinegar but an orange patina appears as it dries. Do I need to somehow get rid of the orange entirely and remove even the paint from the small gaps it's stuck in? Or can I just prime it and paint as-is?
The orange patina is almost certainly iron(iii) acetate, which is the main reaction product of vinegar (acetic acid) and iron. It's a vivid orange-brown colour. It shouldn't affect paint adhesion if it's just a thin film.
Degreasing is the most crucial stage of paint prep. Use something like acetone or isopropyl alcohol and don't handle the part with your bare hands after degreasing. This is particularly important for cast iron, which is inherently porous.
An etch primer will give good adhesion over bare metal or paint, so don't worry about removing every last scrap of paint. If it's hard to remove, then it has good adhesion to the base metal and will give good adhesion to subsequent coats of paint. As long as you've removed the loose paint, you should be fine.
the orange patina could also be flash rusting, whatever it is use wet and dry sandpaper to remove it before painting, use it dry.
I'd caution against etch primer over old paint, I've had reactions with enamel paint and acid etch in the past, also acid etch isn't really required on ferrous metals