We report, for a rodlike nematic liquid crystal with small positive dielectric and conductivity anisotropies, and in the 90°-twisted configuration, low frequency (<2 Hz) square wave electric field generated Carr-Helfrich director modulation appearing transiently over a few seconds at each polarity reversal and vanishing almost completely under steady field conditions. Significantly, the instability is polarity sensitive, with the maximum distortion localized in the vicinity of the negative electrode, rather than in the midplane of the layer. This is revealed by the wave vector alternating in the two halves of the driving cycle between the alignment directions at the two substrates. Besides the Carr-Helfrich mechanism, quadrupolar flexoelectric polarization arising under electric field gradient is strongly indicated as being involved in the development of the transient periodic order. Similar transient instability is also observed in other nematic compounds with varying combinations of dielectric and conductivity anisotropies, showing its general nature. The study also deals with various characteristics of the electro-optic effect that emerge from the temporal variation of optical response for different driving voltages, frequencies, and temperatures.