Small Transport
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 90; Flight Crew Total 4300; Flight Crew Type 800
Communication Breakdown; Situational Awareness; Time Pressure
Conflict NMAC
Flight Crew Took Evasive Action
Environment - Non Weather Related; Human Factors
After canceling IFR on a visual approach into ZZZ; we switched to CTAF and began making position reports. Center had advised us of 2-3 aircraft in our vicinity as we approached the airport. We had one aircraft in sight and were looking for the others. There were several aircraft on the CTAF and no immediate conflicts were noted until a departing aircraft was shown on the TCAS display at 12 o'clock and climbing towards our altitude followed by an automated 'traffic' callout. We could not see it immediately or infer its exact course so started a slight right turn away from the airport to avoid [it]. After several seconds I spotted the other aircraft on a converging course from the left and advised my copilot to increase descent to increase separation as he continued flying and searching out my window. It was difficult to spot due to very little relative movement and it was more difficult to spot from the copilot's seat. During the correction I saw that we were on a collision course and directed a climb/level off before taking [the] controls and beginning a more aggressive climb. My copilot spotted the aircraft immediately after the control transfer and we passed approximately 500 feet above the other plane. I had the opportunity to discuss with the crew of the other aircraft on the ground. After checking in with Center and receiving a traffic advisory; it seems they saw us before our initial ('blind') right turn and began a left turn to increase separation; then a level off to allow us to pass above. The mirrored lateral and vertical corrections contributed to the closure. Our 'blind' turn was initiated due to the TCAS return; which displayed their position and climb; but no lateral movement information. Lateral movement information may have provided better situational awareness in this case. Spotting the aircraft sooner would have also helped prevent the conflict.
Part 135 Captain reported a NMAC while on approach.