Turbulent and compressed sheath regions preceding interplanetary coronal mass ejections (ICMEs) strongly impact electron dynamics in the outer radiation belt. Changes in electron flux can occur on timescales of tens of minutes, which is difficult to capture by a two-satellite mission such as the Van Allen Probes (RBSP). The recently released Global Positioning System (GPS) data set has higher data density owing to the large number of satellites in the constellation equipped with energetic particle detectors. Investigating electron fluxes in a wide range of energies and sheaths observed from 2012 to 2018, we show that the flux response to sheaths on a timescale of 6 hours, previously reported from RBSP data, is reproduced by GPS measurements. Furthermore, GPS data enables derivation of the response on a shorter timescale of 30 minutes, which further confirms that the energy and L-shell dependent changes in electron flux are due to the impact of the sheath. Sheath-driven loss is underestimated over longer timescales as the electrons recover during the ejecta. We additionally show the response of electron phase space density (PSD), which is a key quantity in identifying true loss from the system and electron energization through wave-particle interactions. The PSD response is calculated from both RBSP and GPS data for the 6-hour timescale, as well as from GPS data for the 30-minute timescale. The response is divided based on the geoeffectiveness of the sheaths revealing that electrons are effectively accelerated only during geoeffective sheaths, while loss is commonly caused by all sheaths.