Whoa. Who knew?
If so, what should we be looking for? It's not a bright star. How far would the second star be from the sun and what kind of mass would do the job of making the equinox precess, or in the Copernican style, making the sun appear to move against the stellar background? At present it is a wave of the hands about some mysterious earth wobble, and that wobble seems like Ptolemaic epicycles. It would be a second Copernican revolution.