I'm curious, do anyone happen to know what states have the shortest amount of time to redeem property purhcased at a foreclosure auctions. I know it varies depending on the state

There are some where you own it at the day of the sale and get a tax deed, not a tax certificate.

The law changes yearly so you need to check with the property tax office in the states you wish to buy. Most states are from one to three years,
You may check out Tennesse

Also remember it is not just "paying" back taxes, you may pay well over the tax amount since it is a auction. If 2000 in taxes is due, you may still have to pay 10,000 or more if this is a good property and there are other bidders.