There is not usually a mechanism to identify when a "vacancy" begins from tax or public records. Many vacant properties later become abandoned properties, and this often occurs when the city does a tax taking of the property for non-payment of taxes. However, that does not inform the date on which the property became vacant. The owner/landlord may well be able to provide and document information regarding when vacancy began, assuming the owner has not abandoned the property. Obviously, dates on which lease payments stopped is useful, but occupancy may have continued after payment stopped. There may also be an action for eviction. It will obviously vary from property to property.