1. Periodic dips in brightness: The most prominent characteristic is a regular, predictable decrease in the overall brightness of the system. This occurs when one star passes in front of the other, blocking some of its light. The depth and duration of these dips depend on the size and brightness of the stars and their orbital configuration.

2. Light curves: By plotting the brightness of the system over time, we get a light curve. Eclipsing binaries have distinctive light curves with the characteristic periodic dips. The shape and duration of these dips reveal information about the stars' sizes, orbital period, and inclination.

3. Doppler shifts: The stars in an eclipsing binary system are also moving towards and away from us as they orbit. This motion causes a shift in the wavelengths of light they emit (Doppler shift). By analyzing these shifts, astronomers can confirm the binary nature of the system and determine their orbital velocities.

4. Spectroscopic observations: Spectroscopic observations can be used to determine the spectral types of the stars, which can help identify whether the stars are sufficiently close together to be eclipsing binaries.

5. Radial velocity variations: Similar to Doppler shifts, radial velocity variations can be observed in the light of the stars. These variations are caused by the gravitational pull of the companion star, and their pattern can confirm the binary nature and indicate an eclipsing system.

In summary: The combination of periodic brightness dips, distinctive light curves, Doppler shifts, spectroscopic observations, and radial velocity variations are all indicators that a star system is an eclipsing binary.