I mentioned something like this...
a while back, but from the very general nature of the comments, I don't think that they are looking for what I would look for... waste heat.
In particular, a galaxy with a civilization in the 2.3-2.5 range would, by definition, have a tremendous portion of its energy being captured in one section, but not in another. A large portion of the captured energy would be re-released as waste heat.
So, if you have, in one part of a galaxy, a substantial and varying red shift compared to others, especially if the lines were light on the absorption lines associated with stars, that would be worth looking at closely.
Unless you go for the Schlock Mercenary, approach, and assume that they are all a bunch of scaredy-cats & run out of the galaxy as fast as they can to avoid detection...