Does petting an egg reduce hatch time?

Ten minutes per pet is small, so on a long incubation the real gain comes from friends. Your own pet and each visiting friend's pet are separate interactions, and every one takes 10 minutes off the remaining timer on that egg.

The catch is the cap. Friends cannot caress the same egg without limit, so a crowd of visitors helps until the limit is reached and then stops helping. Spread the attention across eggs rather than piling it onto one.

There is also a separate one-off reduction: placing an egg into the Home Hatcher takes 10 minutes off its timer, once per egg. Taking the egg out and putting it back does not earn it again.

Getting friends to pet your eggs

The petting happens in your Homeland, so a friend has to visit your Home to do it. While there they can also tend your garden and speed it up, which makes a visit worth more than the egg alone. Visiting a friend's Home also raises your Affinity with them, so returning the favour builds the friendship on both sides.

You can do the same for them. Petting another player's incubator cuts 10 minutes from their egg, under the same limit.

Not settled: The exact number of times friends can caress one egg is not stated, so the most time visitors can save on a single egg is not known.