Among active galactic nuclei, blazars show extreme variability properties. We here investigate the case of the BL Lac object S4 0954+65 with data acquired in 2019-2020 by the Transiting Exoplanet Survey Satellite (TESS) and by the Whole Earth Blazar Telescope (WEBT) Collaboration. The 2-min cadence optical light curves provided by TESS during three observing sectors of nearly one month each, allow us to study the fast variability in great detail. We identify several characteristic short-term time-scales, ranging from a few hours to a few days. However, these are not persistent, as they differ in the various TESS sectors. The long-term photometric and polarimetric optical and radio monitoring undertaken by the WEBT brings significant additional information, revealing that i) in the optical, long-term flux changes are almost achromatic, while the short-term ones are strongly chromatic; ii) the radio flux variations at 37 GHz follow those in the optical with a delay of about three weeks; iii) the range of variation of the polarization degree and angle is much larger in the optical than in the radio band, but the mean polarization angles are similar; iv) the optical long-term variability is characterized by a quasi-periodicity of about one month. We explain the source behaviour in terms of a rotating inhomogeneous helical jet, whose pitch angle can change in time.
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