Is this the correct hardware for pin style calipers?

I'm curious as to how you confirmed 3/8-24? You need an sae tap and die set and somebody who knows how to use it to save your new pins with a die and debur the brkt threads with a tap. If something won't screw together by hand at least a few threads, something is wrong. Anybody with an older car should have a bench grinder with a wire wheel to clean threads, a tap and die set, and a jar of copper anti-seize for most hardware.

Never buy a tap and die set that has the sizes embossed in the taps. Middle of the road price sets are fine then when the taps wear out, replace those individually with high quality taps.