Online dating is a bit of a misnomer. Most people are not actually looking to go on dates "online." Instead, online dating is more like attending a massive cocktail party, where you introduce yourself to several people, chat briefly, and then transition to an actual date if you sense some potential chemistry with someone.
As an online dating photographer, I encourage my clients to keep this in mind and present themselves in their first few photos as if they were meeting someone for the first time.
If someone walked up to introduce themselves, it would be weird if they turned and started gazing off into the distance. Yes, you may get some matches from the photo in which you’re looking away from the camera, suggesting an air of mystery, but the stronger, more effective play is to use an image in which you’re looking your potential date in the eyes and giving them a warm, welcoming smile that says “You have my full, undivided attention, and I’m excited to meet you.”