We analyze spectropolarimetric data of the pre-cataclysmic variable binary system V471 Tau obtained with ESPaDOnS at the Canada-France-Hawaii Telescope in two observational campaigns (in Nov/Dec 2004 and Dec 2005). Using Zeeman-Doppler Imaging, we reconstruct the distribution of brightness map and large-scale magnetic field of the K2 dwarf at both epochs, as well as the amount of differential rotation by which surface maps are sheared. We detect significant fluctuations in the surface shear between the two campaigns. It goes from about twice the solar differential rotation rate to less than the solar value in a one-year interval. We conclude that the differential rotation fluctuations obtained for the K2 dwarf resemble those detected on the single-star analog AB Dor, although even larger amplitudes of variation are seen in the K2 dwarf of V471 Tau. Finally, we show that the differential rotation results obtained in this work do not favor an Applegate mechanism operating in the V471 Tau system, at least in its standard form, but leave room for explaining the observed orbital period fluctuations with exotic forms of similar phenomena based on dynamo processes operating within the convective zone of the K2 star.