  Using two years of data from the TESS space telescope, we have investigated
the time series of 633 overtone pulsating field RR Lyrae (RRc) stars. The
majority of stars (82.8 per cent) contain additional frequencies beyond the
main pulsation. In addition to the frequencies previously explained by the
$\ell = 8$ and $\ell = 9$ non-radial modes, we have identified a group of stars
where the additional frequencies may belong to the $\ell = 10$ non-radial
modes. We found that stars with no additional frequencies are more common among
stars with shorter periods, while stars with longer periods almost always show
additional frequencies. The incidence rate and this period distribution both
agree well with the predictions of recent theoretical models. The amplitude and
phase of additional frequencies are varying in time. The frequencies of
different non-radial modes appearing in a given star seem to vary on different
timescales. We have determined a 10.4 per cent incidence rate for the Blazhko
effect. For several stars we have detected continuous annual-scale phase change
without significant amplitude variation. This type of variation offers a
plausible explanation for the `phase jump' phenomenon reported in many RRc
stars. The main pulsation frequency could show quasi-periodic phase and
amplitude fluctuations. This fluctuation is clearly related to additional
frequencies present in the star: stars with two non-radial modes show the
strongest fluctuations, while stars with no such modes show no fluctuations at
all. The summation of the phase fluctuation over time may explain the O-C
variations that have long been known for many non-Blazhko RRc stars.
