..or, do not!
What I mean is this: for a character portrait, you do not necessarily need eye contact.
In fact, often, there is more of a story – more intrigue, more for viewers to work out for themselves, i.e. a more successful picture – if there is no eye contact. Like here (still from that shoot a few days ago):
Or, let’s go crazy and not even incorporate the face at all:
Can you see that these are good people shots?
Now of course I am not saying “never show eyes looking into the camera” – of course not. But do try to not just shoot people looking into your eyes.
If you want homework: do a portrait without eye contact – one that makes me work out the story.