I bought a new OEM exhaust manifold off ebay, I think the label said it was from the 80s (I don't have it here in front of me). There's a threaded fitting about half way down, below the choke pocket...so the back side a couple inches up from the flange.

First off, what is that for?

Second, what plug or bolt size do I need to plug that off? It looked like a 3/8" pipe plug but it was a little loose and bottomed out (didn't plug)

Sounds like you're describing the approximate location of the O2 sensor bung.
Your local exhaust shop or parts house should be able to fix you up with the appropriate size metric thread plug.

Roger

Dorman 65220 oil pan plug (18mm x 1.5 thread, 19mm hex head)

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Ed
64 Valiant 225 / 904 / 42:1 manual steering / 9" drum brakes

Thanks that worked perfectly!