I did my due diligence, and found that everything except the following was deprecated:
brew install sphinx@1.4.13
Error: No available formula with the name "sphinx@1.4.13"
==> Searching for a previously deleted formula...
Error: No previously deleted formula found.
==> Searching for similarly named formulae...
Error: No similarly named formulae found.
==> Searching taps...
Error: No formulae found in taps.
But none of the documentation explained what the current process is for moving forward at this point. Should I hunt for the specific commit, and follow that old process? Does it apply in the case when, potentially, the theoretical tap you would need isn't popular enough for that version to be maintained?
Edit: There are several things called "sphinx" and confusing one for another screwed me up. This question was meant to resolve an issue I ran into with a Rails project and the thinking-sphinx gem, which I was using version 1.4.13 of. I'd attempt to run the Rails server and it would complain about Sphinx not being installed. As it turns out, the project I was supposed to be working on doesn't even use thinking-sphinx, so I won't have time to even clarify the issue.