Vanishing Airplane

I had an odd experience yesterday, holding at an uncontrolled airport. I taxied out in calm winds and then was asked to stay on the ground while someone in the back made a telephone call to confirm something. It's like driving a limo sometimes, except with the roar of the engines instead of the glass partition separating me from the back. While the telephone call was going on, the wind picked up and I was now at the wrong end of the runway. I was willing to take a few knots tailwind, but there were aircraft arriving so there were other safety issues involved in the runway choice. I checked with the back and they were now waiting for a call to be returned, so I had time to taxi back to the other end. I describe all this merely as preface, to indicate that I had been on frequency for a while and picked up a situational awareness for who was coming and going.

Sitting in the runup area at the correct end of the runway, with enough room for others to taxi around me if need be, I heard an airplane call inbound to the field, giving his ETE as 11 minutes. It was three minutes to nine at that point, so I wrote down his call sign and 9:07 on my kneeboard. That would give me an idea of when he was due, to help me not taxi out in front of him. A few minutes later he called again, seven minutes back. It was nine on the dot, so his ETA was unchanged. A few minutes later the cellphone conversation was over, the destination confirmed, and the cabin ready for takeoff. I called the inbound airplane by callsign for a position report. No response. Just in case I got his callsign wrong, I called again referring to him by destination and type. No response. He didn't answer on either the aerodrome frequency or 126.7. I would have seen him had he landed in front of me on the into wind runway. There was a possibility he had landed the other way, with a tailwind, but there was no taxiway between the one at the threshold, and mine. So he landed very short despite a tailwind and turned around to backtrack off the runway without making any of the required downwind, final, backtracking and clear calls? Unlikely. There would also be no advantage to backtracking: the two taxiways are equally inconveniently located to the apron.

I determined that whatever had happened to him, there was no conflicting traffic, and I took off. My current theory is that he accidentally used the wrong aerodrome name in his calls, and he was descending into some other aerodrome sharing the same frequency. Once he reached circuit altitude I stopped hearing his transmissions, and he could not hear mine.

Or he found himself suddenly in the Bermuda triangle, where he took advantage of the international card in his GPS and landed somewhere hospitable where he and his passengers are enjoying fruity drinks with umbrellas.