In my experience, someone who is actively lobbying to be a moderator may be a poor choice. There is a tendency for control freaks to seek out opportunities for power and control, and it doesn’t work out well. I look for people who work to facilitate discussion even though they aren’t moderators.
Emotional Intelligence/Customer Service Skills - This is the most important: Are they capable of being nice to people who are not being nice to them?
Empathy matters, but so does the ability to set aside criticism. I’ve had some really great mods who were very empathetic, but the conflict and nastiness they had to deal with hurts them too much, and they had to quit because of this (and rightly so).
If you have a low-conflict forum they should be OK.