@Doug Farmer The property does not have to be vacant, but yes you have a short amount of time to get moved in (60 - 90 days). You could buy a leased duplex and keep one tenant and vacate the other depending on their lease structures or you can buy a tenant out of their lease (usually doesn't cost much). I have only purchased vacant duplexes for my personal investments, but several of y clients have purchase fully leased properties and then moved into them. I don't advocate skirting the law, but FHA isn't check to make sure you are fully moved into the unit in the specified amount of time. If you move in is a few days off I don't see this as an issue (it's more about intention).
One issue I have run into has been buying a distressed duplex that would not meet FHA guidelines without improvements. In my specific case I was buying a HUD foreclosure and 2 days after I put it under contract someone stole all of the copper pipes and the HVAC coils. HUD would not replace the copper nor would they offer a discount because they had multiple offers. In this case I was allowed to use a "repair escrow," close on the property, and had to complete repairs and have a HUD rep inspect prior to moving in. Essentially I closed and repaired, but did not take possession until repairs were completed. Keep in min HUD will only allow a certain amount of "repair escrow" in this case it was around $5K in repairs.