We explore the environmental dependence of star formation timescales in low mass galaxies using the [\(\alpha\)/Fe] abundance ratio as an evolutionary clock. We present integrated [\(\alpha\)/Fe] measurements for 11 low mass (\(M_\star \sim 10^9~M_\odot\)) early-type galaxies (ETGs) with a large range of cluster-centric distance in the Virgo Cluster. We find a gradient in [\(\alpha\)/Fe], where the galaxies closest to the cluster center (the cD galaxy, M87) have the highest values. This trend is driven by galaxies within a projected radius of 0.4~Mpc (0.26 times the virial radius of Virgo~A), all of which have super-solar [\(\alpha\)/Fe]. Galaxies in this mass range exhibit a large scatter in the [\(\alpha\)/Fe]--\(\sigma\) diagram, and do not obviously lie on an extension of the relation defined by massive ETGs. In addition, we find a correlation between [\(\alpha\)/Fe] and globular cluster specific frequency (\(S_N\)), suggesting that low-mass ETGs that formed their stars over a short period of time, were also efficient at forming massive star clusters. The innermost low-mass ETGs in our sample have [\(\alpha\)/Fe] values comparable to that of M87, implying that environment is the controlling factor for star formation timescales in dense regions. These low-mass galaxies could be the surviving counterparts of the objects that have already been accreted into the halo of M87, and may be the link between present-day low-mass galaxies and the old, metal-poor, high-[\(\alpha\)/Fe], high-\(S_N\) stellar populations seen in the outer halos of massive ETGs.