Flight Crew Air Transport Pilot (ATP); Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Multiengine
Flight Crew Last 90 Days 100; Flight Crew Total 16850; Flight Crew Type 415
Situational Awareness
Conflict Ground Conflict; Less Severe; Ground Incursion Runway
Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action
Human Factors; Airport
Dropped off passengers at Cuyahoga County Airport (CGF). Only the two pilots [were] on board.We got our IFR clearance to head back to the home airport. [It is] about a 15 minute flight.  [We] got a taxi clearance to taxi to Runway 6. Tower was about to close. While taxiing; Ground Control let us know we had about 30 seconds till they would close and to use the Ground frequency of 121.85 to contact CLE ATC for release. That was the first link in the chain of events; tower facility closing.Second link; my copilot didn't hear the correct frequency to contact CLE ATC on. He was going to use 118.50. I let him know it was 121.85; but he insisted it was the other. We went back and forth on that 3 times. So; I let him use 118.50. Figured he would figure it out when he tried; and he did as Tower let him know it was 121.85. That ate up a good 30 seconds or more of time. We got our release time from CLE. Jumping from frequency to frequency; thought I heard the aircraft make a call in the pattern.Third link; as we taxied out; we were notified of an aircraft in the pattern. [We] didn't know [the] exact position of it; but knew it was there.Fourth link; after landing and then taxiing back out; the side windows were slightly fogged over from our decent on the inbound flight. Cold soaked windows [and] warm moist air caused the side windows to begin to fog over.Fifth link; since we knew of an aircraft in the pattern; I asked on the frequency if there was anyone on Final Approach to Runway 6 at Cuyahoga. No reply.It all added up; copilot and I looked for an aircraft on final before we transmitted we were departing Runway 6. Again; no reply from inbound aircraft. [We saw] no landing lights in the sky from the approach direction to Runway 6; possibly due to the side window starting to fog over. Or; maybe the inbound aircraft wasn't yet directly in line for a straight in approach? No idea; either way; we saw no lights. We started to taxi for the runway.Next we heard the Ground Controller say to the aircraft in the air to make a right 360. I immediately stopped our aircraft. We were across the hold line with the tail of the aircraft at about the hold line position. The nose of our aircraft was not on the runway itself; but theoretically; we all know; once past that hold line an aircraft is still considered on the runway. In that position; copilot and I saw the lights of the inbound aircraft turning south in what appeared to be their 360 turn. Looked to be a quarter mile or so away. At that point in time; I chose to make another call that we were departing Runway 6. I decided best to get our aircraft out of the approach end environment of the runway completely. Still heard no reply from the inbound aircraft.Several things that added up.I should have simply waited and waited and waited till the aircraft in the pattern was on the ground.Before the Tower closed; they could have given a position report on the pattern aircraft; or maybe I missed that if they did. Or; possibly saying to us; it would be advised to wait till the inbound aircraft landed as is was on a close base or such.Hearing the proper frequency by the copilot would have given a better opportunity to get things right first time instead of trying to find the right freq.Inbound pilot could have replied when asked if anyone was on final; or could have spoken up when we advised we were about to take off. Maybe [they were] student pilot(s); low time; or just distracted with work load.Glad the Ground Controller was still listening in on the frequency and told the inbound aircraft to make a 360 turn. That broke the chain of events. Tower closing and switching of who to talk with an aircraft in the pattern; improper radio frequency; simple confusion. One thing leads to another. Best to hold position until all knows what is going on.
Corporate Captain reported traffic conflict with an inbound aircraft just as the Tower was closing.