Simple question..

Forgive my lack of knowledge w/regard to O/B parts,
still learning my way around. But what is this part called
(the rod in the red box attached to the primer assembly)?

From what I can see, it appears to be the link wire for the fast idle.

it would help if we knew - the make- year and hp of motor --

It's a 1994 Mercury 25hp.

If it's working properly, you should be able to rotate the primer knob cw and ccw and see the link wire move front to rear.

eggzactly what he sed --- :mrgreen:

Found it!
In a parts diagram I was directed to on Boats.net.
It's called an "idle wire."

Well, the reason I ask is that mine is gone. I noticed that turning
the knob had no noticeable effect on the engine. Pulled the cowling
off and noted the assembly moves but it's not attached to anything
due to the missing rod. No idea where it went, it's probably down in
there somewhere. Didn't have much time to dig around or good lighting
when I noticed last night.

At least I know where to order a new one now!