How to tell if a planet with twin suns orbits one or both of them?

An experienced space time traveler teleports from place to place and planet to planet with a vehicle or using psychic powers. Now suppose that this traveler teleports to a habitable planet.

Suppose that he sees twin suns in the day sky, close together. By twin suns, I mean they seem to have identical apparent diameters and identical colors, to the best of the traveler's vision. They also appear very close together, so it is easy to compare them and think of them as twin suns.

If the spacetime traveler stays on the planet for a while, how could he/she determine if the planet orbits both suns or orbits one of them with the other sun farther away? How long would that method take?

Assume that the traveler doesn't have an astronomical radar device to directly measure the distance to each sun.

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How to tell if a planet with twin suns orbits one or both of them?

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