Final answer:
Evidence for multiple starbursts in small Local Group galaxies includes stars of different ages indicating different starburst periods and patterns of star formation indicating past collisions, as observed in Stephan's Quintet.
Step-by-step explanation:
The evidence suggesting that small galaxies in our Local Group have undergone two or more starbursts in the past is that we see small galaxies in which many stars have one age and many others have another age that is billions of years older.
This is seen in cases on Stephan's Quintet, where different age ranges of star clusters within these galaxies suggest multiple periods of intense star formation. Furthermore, the galactic collisions triggered significant increases in star formation, as in the case of Stephan's Quintet, where galaxies interacting gravitationally caused bursts of star formation with clusters aging from 2 million to 1 billion years old.
This is in line with what researchers find when observing young galaxies far away, which exhibit multiple intense knots and clumps of bright starlight associated with high rates of star formation, much like starburst galaxies.