I've made an EGG-celent discovery!!
The egg hunt resets every 72 minutes! I found this out by testing my theory that, since we only have 20 chances a day, I could divide 24 hours by 20 chances = 1.2 hours, which is also 72 minutes. SO! Egg hunt resets every 72 minutes (1hr 12 min.).
^I feel like a scientist with that entire blurb I just typed out xD