I would think that your old fender mounted starter relay welded the contacts closed.
I don't think they should rattle. Have you tried testing for continuity across the lugs?
Re: correct wiring.
Small blue/red push-on connector to the (S) terminal.
Starter cable to one lug.
Everything else to the other lug.
There were some Bullnose that used a fuselink attached to the (I) terminal, providing full voltage to the fuel pump but I don't think you have that.
Jim,
Lil'Red is a '87 F250 HD, 4.10's, 1356 4x4, Zf-5, 3G, PMGR, Saginaw PS, desmogged with a Holley 80508 and Performer intake.
Too much other stuff to mention.