There is a more consistent way if you are willing to manip RNG.
Auto-petters can be dropped from boss monsters in the dangerous mines. What a boss monster drops is determined by the tile it dies on.
If you find a boss monster, you can fence it in to restrict its movement, then kill it. My predictor (Map Predictor on Nexus mods) can show you what tile the monster needs to die on.
Other than that, the brute force method in the caverns that has been mentioned is your best bet.