What is the "one-in one-out" FAA rule for IFR traffic landing or departing at an airport without a tower or at an airport with a closed tower?
Several sections of the AIM give guidance on this. It is explicitly stated that only one aircraft at a time is given a departure clearance. It is implied that there would be no approach clearances until the departing aircraft’s position is known by ATC.


  4−4−1. Clearance   
  
  a. A clearance issued by ATC is predicated on known
  traffic and known physical airport conditions. An ATC clearance means
  an authorization by ATC, for the purpose of preventing collision
  between known aircraft, for an aircraft to proceed under specified
  conditions within controlled airspace.
  
  5−2−6. Departure Restrictions, Clearance Void Times, Hold for Release,
  and Release Times a. ATC may assign departure restrictions, clearance
  void times, hold for release, and release times, when necessary, to
  separate departures from other traffic or to restrict or regulate the
  departure flow.
  1. Clearance Void Times. A pilot may receive a clearance, when operating from an airport without a control tower, which contains a
  provision for the clearance to be void if not airborne by a specific
  time. A pilot who does not depart prior to the clearance void time
  must advise ATC as soon as possible of their intentions. ATC will
  normally advise the pilot of the time allotted to notify ATC that the
  aircraft did not depart prior to the clearance void time. This time
  cannot exceed 30 minutes. Failure of an aircraft to contact ATC within
  30 minutes after the clearance void time will result in the aircraft
  being considered overdue and search and rescue procedures initiated.
  
  NOTE−
  1. Other IFR traffic for the airport where the clearance is issued is suspended until the aircraft has contacted ATC or until 30 minutes
  after the clearance void time or 30 minutes after the clearance
  release time if no clearance void time is issued.
  
  5−5−4. Instrument Approach
  
  b. Controller.
  1. Issues an approach clearance based on known traffic.
  
  5−5−4. Instrument Approach a. Pilot.
  1. Be aware that the controller issues clearance for approach based only on known traffic.