Are there jobs that can be had by beating out the competition in tests of general knowledge?

I'm semi-retired, after having worked for 25 years as an economist and real estate investment officer. I score quite high on tests of general knowledge, and I'm a good communicator, in both oral and written formats. I would like to apply these skills to a part-time or full time job. I'm willing to travel, and I'm flexible with respect to location and hours. I'm also a private pilot, and I own a small, bush-type airplane.

You could try out for Jeopardy. You could also be a tutor.

You should try to get on jeopardy. Ken Jennings did pretty well for himself. Otherwise, try consulting in your field of expertise. I find that a lot of consulting work is drawing upon your own opinions and past experiences. It can be challenging and fun work.

Yes. I like your attitude. You wont need to look far. Don't go where you wouldn't be really really happy just to get a "Job". You have what a lot of companies need.