https://www.cnet.com/news/nasas-curiosity-rover-sees-a-solar-eclipse-on-mars-after-sunset/

Actually spotting the over-the-horizon eclipse took some involved image analysis. Basically, the dusk light the sun projects upward after setting briefly dimmed over the course of a few minutes. Ellison shared the above GIF animation, which is essentially a time-lapse of the event. When sped up this way, the projected eclipse can clearly be seen. 

Ellison also cross-referenced the photos with NASA's Horizons database tracking the orbits of thousands of solar system objects to verify it was in fact Phobos passing in front of the sun that caused the effect.