According to the Minecraft Wiki,
Patrols can spawn during the day on blocks with a block light level of 8 or lower. If a player is within 5 by 5 by 5 sub-chunk cube around a village, patrols do not spawn.
The game picks a random location 24–48 blocks along each of the X and Z axis away from the player to try to spawn the patrol's captain. If a pillager cannot spawn at the chosen position, it gives up and does not spawn anything. If the captain can spawn, the game tries to spawn 1 + localDifficulty [verify](rounded up) more pillagers, with each pillager spawning within a 4-block radius square around the previous pillager.
So, if you find a large open area and wait for long enough, a pillager patrol will spawn.
Please note, that Pillager Patrols only spawn when your world reaches 100 minutes or 5 in-game days. The game will attempt to spawn a pillager patrol every 10 ish minutes with a success rate of 20%.
So in theory, if you find a large open area, you should be able to find a pillager patrol in 10 minutes if you're lucky, or up to 50 minutes if you aren't.