Electron-positron pair production from vacuum in a strong electric field oscillating in time is studied. The field is assumed to consist of two consecutive pulses, with variable time delay in between. Pair production probabilities are obtained by numerical solution of the corresponding time-dependent Dirac equation. Considering symmetric field configurations comprising two identical pulses, we show that the pulse distance strongly affects the momentum spectra of produced particles and even the total production probability. Conversely, in a highly asymmetric situation when the field contains low-intensity prepulse and high-intensity main pulse, we identify a range of field parameters where the prepulse despite its weakness can leave visible traces in the particle spectra.