Year marking astronomical event with extreme perihelion precession

For us earthlings, the concept of "year" came from the observation that the Sun reaches a minimum and a maximum span in the rise-set path in the sky.

On a planet experiencing extreme perihelion precession (about 30 degrees) is there any recurring astronomical event which can mark the end of a year for the inhabitants of the planet? (picture is meant to illustrate the extremity of the precession, not the eccentricity of the orbit)

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Year marking astronomical event with extreme perihelion precession

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