  Variability of a galaxy's core radio source can be a significant consequence
of AGN accretion. However, this variability has not been well studied,
particularly at high radio frequencies. As such, we report on a campaign
monitoring the high radio frequency variability of 20 nearby, cool-core
brightest cluster galaxies. From our representative sample, we show that most
vary significantly over timescales of approximately one year and longer. Our
highest cadence observations are at 15 GHz and are from the Owens Valley Radio
Observatory (OVRO). They have a median time interval of 7 days and mostly span
between 8 and 13 years. We apply a range of variability detection techniques to
the sources' lightcurves to analyse changes on week to decade long timescales.
Most notably, at least half of the sources show 20 per cent peak to trough
variability on 3 year timescales, while at least a third vary by 60 per cent on
6 year timescales. Significant variability, which is important to studies of
the Sunyaev-Zel'dovich Effect in the radio/sub-mm, is therefore a common
feature of these sources. We also show how the variability relates to spectral
properties at frequencies of up to 353 GHz using data from the Korean VLBI
network (KVN), the NIKA2 instrument of the IRAM 30m telescope, and the SCUBA-2
instrument of the James Clerk Maxwell Telescope.
