Your "last US residence" is meant to be your domicile.   

Under traditional rules and state law, a person is permitted to register and vote only in the place that constitutes his/her domicile. Different rules apply to active duty servicemembers, but when a civilian moves from one place to another, with the intent to make the new place home for a significant time, the individual's domicile changes to the new place. However, leaving place A to go to place B for a temporary purpose, with the intent to return to place A or to move to still another place when the temporary purpose has been fulfilled, does not amount to a change of one's domicile.