I'm a guitar player, but I'm considering getting singing lesson because I think it would improve my ear for music. I'm not looking to be the next Pavarotti or the local karaoke king. Would this alienate me from most singing teachers? What should I be looking for in a singing teacher?
I don't know much about singing teachers, but if you came to me for guitar lessons I wouldn't care if voice were your primary instrument. I also wouldn't care if you had no plans to become the next Jimmy Page or Tom Morello. If you just wanted to learn to do one song ok, I would still teach you because I would expect you would say "ok, I'll learn one more song" when you are done with the first one, and so on.
I would look for price, appropriate time availability, ability to teach the style of music you want to learn, and good personality fit for pretty much any teacher. An offer of a free intro lesson is nice becuase it shows awareness that not all student-teacher pairing make a good fit, and it's nice to audition teachers. Be a little skeptical of anyone charging a very low rate - they might have to in order to retain students and that's not a good sign.
There's a case on this here: Criteria for selecting a voice teacher
I think any voice coach is just happy to help, no matter what your background or future plans. I think studying multiple instruments is aways an incredibly helpful and good thing to do, both for your creativity as well as your overall musical comprehension. If I was a voice coach, I'd actually be a bit worried if someone whose primary instrument isn't voice, would come up to me and say "I'm definitely going to be the next Pavarotti, ok?" A coach always admires you for understanding that you might not be able to learn everything all by yourself, but you've decided to reach out to someone who can actually guide you to the right direction.
Whatever you're learning, you'll be more likely to stick to it and get more out of it if your teacher is actually a great personality whom you get along with well. Openly talk to candidates about your experience and wishes, and see how well they respond: Do they seem to understand your place well, do they seem cold and distant or personally concerned and innovative in terms of how they could help you. I would also want to actually check their background and be sure that they are professionally trained and credible in voice pedagogy. Any person with a functioning voice can technically perform the act of singing, but under different conditions, some people who train on their own by mimicking others, can unawarely inflict physical harm on their vocal system. When their methods aren't corrected by a credible teacher, they become habits and on the long run can inflict permanent damage to the voice. Singing is like sports: If you've never lifted weights, you do not look at the Olympic pros and go straight at forcing yourself to lift 100kg just because you saw them do it and it seemed cool. Voice is an instrument which has to be trained like muscles, there's a good reason why you have to start gradually, do your exercises, build a good foundation. There is no shortcut to just imitating the coolest and most radical singers that the world has, they have a solid background. Since you are a student, I think it's absolutely crucial that your voice coach is a trained professional, not someone who just started singing and would love to tell others how to do it by mimicking and following hunches. Some coaches swear on specific trademarked singing methods in which they teach. If your teacher candidate is a certified coach of some specific method, my tip is to avoid "products" which are sold to you as "learn to sound like the craziest pop and rock singers instantly and without barely any effort". If that was sports, the equivalent would be "lose 30kg and gain perfect abs in one night with no effort". Don't trust a teacher who promises quick shortcuts in achieving a physical transformation.