It is overpowered af but don't use it to get money. Use it to get the charisma glasses and each of the others during your first 12 hours (coincidently, they will all be close and easy to grab). Then attempt to write out an exhaustive list of any other objects or abilities that might threaten you (or maybe start with this one, as the glasses are the only one that threatens you from the original list). I'd say hopefully no one else has some other object or ability that warns them of anything that might threaten them, but yours might nullify theirs during your 12 hours. Attempt to deal with the list before half the time has passed.
Then start attempting to gain new abilities. Or attempt to find 28 more coins. 28 instead of 27 so that you can flip the next coin before the current one runs out and never fail the next flip. The sleep mask ensures you never sleep through a transition. Not that you'll even need the ability to be constantly active.
Yeah I was going to choose the sleep mask until I saw the coin. If everything goes my way then I effectively have the powers of the glasses and the frying pan, plus unlimited luxury from lotteries, discoveries, opportunities, etc. The cooldown needs to be nerfed, or maybe add a negative debuff to the tails side.