ASRS 1743912

Upon IFR departure from SJT tried to pickup IFR clearance from both FSS frequency listed and DFW frequency. Unable to get clearance on ground. At this time local Tower and Approach/Departure Control had closed. [I] decided to depart VFR and pick up clearance in the air. It was a clear night with no reported traffic so departed VFR off of Runway 18. Set initial climb alt to 17,500 ft. At about 10 NM noticed alert from iPad that TFR was ahead. Ended up clipping NW corner. As soon as error was noticed immediate corrective action was taken to clear TFR. Time in TFR estimated at less than 20 seconds. Tower/Approach states "When you're talking with us, you can proceed through the TFR." We are normally talking to ATC, and routinely fly through the TFR without thinking about it - developed complacency toward the TFR. Tower/Approach control had just closed. Just before Tower closed, we heard an arriving aircraft ask about the TFR, and Tower reported that the area was not in-use and allowed the aircraft to fly through the TFR. Was unable to reach FSS or Center on the ground to open flight plan/talk to ATC. Elected to depart VFR and pick up IFR enroute. Had TFR displayed on moving maps on both iPads. Did not get our attention (factors: complacency mentioned above, fatigue after long flying day, just a ferry home). The TFR should have been displayed graphically on the aircraft's moving map, but the XM weather subscription recently expired. "TFR" option was selected for display but not receiving XM data. Saw another aircraft in TFR; didn't occur to us it was a military drone until they called on radio. Having never operated there at night, maybe had assumption they wouldn't be flying when Tower closed.