Flight Crew Air Transport Pilot (ATP)
Ground Incursion Runway
Human Factors
Upon landing at GGG; the winds were gusting to 30 knots; and we had 10 knot loss short final. The First Officer (FO) landed smoothly but long trying to counter the effects of the wind. Construction was taking place along taxiway Golf and the exit at November was closed. At taxiway Bravo there were several ground ops vehicles giving the illusion that Bravo was closed as well. The FO slowed the aircraft prior to runway 36 as we waited for the tower to give us taxi instructions; but the tower was busy with a back and forth transmission with another aircraft that was inbound to the airport. The transmissions continued long enough that we taxied and tried to exit runway 36 un-commanded by the tower onto runway 31 and exited at Lima for the ramp. It was at this time that the tower informed us that they considered this to be a runway incursion and a pilot deviation; and to call the tower.The only choice that we had was to stop on the runway prior to runway 31 and wait for the transmissions to cease between the tower and the other aircraft and ask for taxi instructions from the tower.
[Report narrative contained no additional information.]
Corporate Jet flight crew reported a runway incursion after landing at GGG due to construction and communication issues.