I'm pretty sure @Cooper and some others said it's based off when you buy them or have them made resetting. If you get something reset at 5:21 it will reset at 6:21, 7:21, and so on.
I think there's a few exceptions to that (maybe custom made stuff, pets, anything you make non-decay+resetting, etc), but anything you buy from the artie shop should reset an hour after you bought it.
Pets and collared mounts have a longer reset time (don't remember exactly what it is), which can be cut in half with a Badge of Returning from the Shop of Wonders. I think it stacks, so you can use two badges for 25% reset time for example.
18 hours reset normally for mounts/custom pets. I feel like the mini pets are much much shorter, but that they also vary.
You can only attach badges of returning to collared mounts, not pets. I idea'd adding in custom pets a while back, which I think? was approved, but nothing has come of it since.
And I love too Be still, my indelible friend That love soon might end You are unbreaking And be known in its aching Though quaking Shown in this shaking Though crazy Lately of my wasteland, baby That's just wasteland, baby
There is a blinding flash as you attach the badge to the collar of a sun-hued kitten. It should now reset to your inventory approximately once every 9 Achaean days.
Looks like it got implemented while I wasn't looking! Awesome.
And I love too Be still, my indelible friend That love soon might end You are unbreaking And be known in its aching Though quaking Shown in this shaking Though crazy Lately of my wasteland, baby That's just wasteland, baby
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VVV Or that, much less confusingly worded.
You can only attach badges of returning to collared mounts, not pets. I idea'd adding in custom pets a while back, which I think? was approved, but nothing has come of it since.
That love soon might end You are unbreaking
And be known in its aching Though quaking
Shown in this shaking Though crazy
Lately of my wasteland, baby That's just wasteland, baby
Edit: It looks like it's always said that though, so maybe the help file is wrong/misleading?
Looks like it got implemented while I wasn't looking! Awesome.
That love soon might end You are unbreaking
And be known in its aching Though quaking
Shown in this shaking Though crazy
Lately of my wasteland, baby That's just wasteland, baby