A natural spawned pillager patrols move on their own speed, but when they spot a player, they will stand still and still look at the player.
However, when you're closer to them, they will start moving normally again.
MC-151910 Vindicators & Pillagers inside an Illager Patrol are not approaching the Player from a certain distance
MC-155651 Illagers will stare at you at a distance but not come to you