When/how do pets want to play? I keep trying (mostly for Major Drills) and all 16 of my pets usually refuse to play with items. Is there something not resetting? Is there something I am missing? I cant recall having this issue as frequently or with as many pets consistently not wanting to play.

Pets will not play with a toy if their Happiness is "10 / 10" just like they won't eat a food if their Hunger is "10 / 10"... Minions keep pets at full happiness.