Patrols spawn every 20 minutes when near villagers iirc. No specific distance or direction that I know off, but try exploring in a 300 block radius of the place you stay at most. Works for me.
Forgot to add that the ones with the banner on the head give bad omen of you kill him. (If you kill him with effects (like fire aspect) it won't give you bad omen). I assumed you already knew though :)