We consider the process of electron-positron pair production in the presence of strong electric backgrounds being rapidly switched on and off and examine the total particle yield. For sufficiently sharp field profiles, the particle number can be substantially enhanced. It is demonstrated that this enhancement is quite similar to the phenomenon of dynamical assistance by a weak high-frequency field superimposed on a strong background. Both these mechanisms are analyzed by means of exact numerical computations, worldline instanton approach, and the locally constant field approximation. We identify the timescale of the switching profile leading to the pair-production enhancement and argue that the particle yield is highly unlikely to be increased by shaping the switch on and off of realistic laser pulses. On the other hand, we confirm that it is feasible to observe the dynamically assisted Schwinger effect by adding a rapidly oscillating field to a strong electric background.