We report on the physical properties of solar sequential chromospheric brightenings (SCBs) observed in conjunction with moderate-sized chromospheric flares with associated Coronal mass ejections. To characterize these ephemeral events, we developed automated procedures to identify and track subsections (kernels) of solar flares and associated SCBs using high-resolution Hα images. Following the algorithmic identification and a statistical analysis, we compare and find the following: SCBs are distinctly different from flare kernels in their temporal characteristics of intensity, Doppler structure, duration, and location properties. We demonstrate that flare ribbons are themselves made up of subsections exhibiting differing characteristics. Flare kernels are measured to have a mean propagation speed of 0.2 km s-1 and a maximum speed of 2.3 km s-1 over a mean distance of 5 × 103 km. Within the studied population of SCBs, different classes of characteristics are observed with coincident negative, positive, or both negative and positive Doppler shifts of a few km s-1. The appearance of SCBs precedes peak flare intensity by ≈12 minutes and decay ≈1 hr later. They are also found to propagate laterally away from flare center in clusters at 45 km s-1 or 117 km s-1. Given SCBs' distinctive nature compared to flares, we suggest a different physical mechanism relating to their origin than the associated flare. We present a heuristic model of the origin of SCBs.