  We report a search for time variations of the solar $^8$B neutrino flux using
5804 live days of Super-Kamiokande data collected between May 31, 1996, and May
30, 2018. Super-Kamiokande measured the precise time of each solar neutrino
interaction over 22 calendar years to search for solar neutrino flux
modulations with unprecedented precision. Periodic modulations are searched for
in a dataset comprising five-day interval solar neutrino flux measurements with
a maximum likelihood method. We also applied the Lomb-Scargle method to this
dataset to compare it with previous reports. The only significant modulation
found is due to the elliptic orbit of the Earth around the Sun. The observed
modulation is consistent with astronomical data: we measured an eccentricity of
(1.53$\pm$0.35)\%, and a perihelion shift of ($-$1.5$\pm$13.5) days.
