What important physical characteristic of the stars, besides the orbital period, is determined by analyzing the timing of eclipses in a light curve?

Answer

The physical sizes of the stars themselves.

By measuring how long it takes for one star to completely cover the other during an eclipse, astronomers can relate the orbital speed (derived from spectroscopy) to the physical sizes of the stars.

What important physical characteristic of the stars, besides the orbital period, is determined by analyzing the timing of eclipses in a light curve?
measurementAstronomerstarmassbinary star system