I'm afraid that this one was a Home Simplson [doh!]

My issue turned out to be that one side of my comparison was nchar

and the other side was char.

I had been "playing with" the bin collations versus the bin2 collations (I'm sticking with bin2), but in the process, somehow, I ended up with nchar versus char. SQL Server must have thought that it was doing an implicit conversion (i.e. no warnings or errors of any kind), but in turn that disabled the index.