Rotation period measurements of stars observed with the Kepler mission have revealed a lack of stars at intermediate rotation periods, accompanied by a decrease of photometric variability. Whether this so-called dearth region is a peculiarity of stars in the Kepler field, or reflects a general manifestation of stellar magnetic activity, is still under debate. The K2 mission has the potential to unravel this mystery by measuring stellar rotation and photometric variability along different fields in the sky. Our goal is to measure stellar rotation periods and photometric variabilities for tens of thousands of K2 stars, located in different fields along the ecliptic plane, to shed light on the relation between stellar rotation and photometric variability. We use Lomb-Scargle periodograms, auto-correlation and wavelet functions to determine consistent rotation periods. Stellar brightness variability is assessed by computing the variability range, R_var_, from the light curve. We further apply Gaussian mixture models to search for bimodality in the rotation period distribution. Combining measurements from all K2 campaigns, we detect rotation periods in 29860 stars. The reliability of these periods was estimated from stars observed more than once. We find that 75-90% of the stars show period deviation smaller than 20% between different campaigns, depending on the peak height threshold in the periodograms. For effective temperatures below 6000K, the variability range shows a local minimum at different periods, consistent with an isochrone age of ~750Myr. Additionally, the rotation period distribution shows evidence for bimodality, although the dearth region in the K2 data is less pronounced compared to the Kepler field. The period at the dip of the bimodal distribution shows good agreement with the period at the local variability minimum. We conclude that the rotation period bimodality is present in different fields of the sky, and is hence a general manifestation of stellar magnetic activity. The reduced variability in the dearth region is interpreted as a cancelation between dark spots and bright faculae. Our results strongly advocate that the role of faculae has been underestimated so far, suggesting a more complex dependence of the brightness variability on the rotation period.