@ JasonB:
My lathe is a Chester DB7VS. That's a "fiddle with change gears" type of machine, rather than selectable gearbox, so it's more likely I can make up a suitable ratio.
@andyf:
The objective is to insert this part into a hole in a block, then screw another dowel into the cross hole (using something like John S suggests) through the block, forming a right angle. Robustness isn't an issue, it's a visual prop that's not going to be strained.
The dowel may be resin coated to help get a glossy finish. That'd also help split resistance.
It is only a 1-off, so learning/acquiring the brazing equipment is a bit too much, methinks.
@Dave BC:
Your comment about epoxy gives me an idea. I could make the pin I want with a machine thread then epoxy it into the part you suggest. That'd also make it easier to adjust the length of the pin - I can keep modifying and trying it until it fits, then epoxy it.
I think we have a winner.

@John S:
The cross-drilled part needs to be too short to screw on as you suggest. As said above, I do intend to use something like you linked to screw into the cross hole in the pin I'm making.