Hello, Vne,
Actually, you can easily 'reason out' the areas to be painted, and those to be left bare (with the thinnest possible coating of a 'rust-resisting' oil such as 'Break-Free' or equivalent.)
That swivel base works by friction, analogous to an 'expanding-wedge' or, if you will, a 'model A Ford' class of mechanical brake system, used by many car makers 90-100-ish years ago.
All the parts should be painted, except for the inner surface of the base, against which the 'brake shoes' bear, the area of the 'shoes' which bears against the inner surface of the base, and the surfaces of the shoes against which the wedge bears, as well as the surfaces of the wedge which act to expand the shoes, and the bore for the 'king-bolt', or 'king-screw' which holds the base to the fixed jaw, yet allows it to swivel freely.
On assembly, the surfaces of the wedge which act to expand the shoes should have a coating of a thick graphite-and-oil mix, or a good commercial anti-seize compound, as should the tapped hole in the wedge for the draw-bolt.
The Parker 'friction-clamping' swivel-base scheme might seem a bit 'weak' to a first glance, compared to the positive 'toothed wedge-bolt' of a Reed, yet it works quite well in practice.
cheers
Carla