That applies to custom controls as well.
PICO-8 includes stat() function allowing to get some extra values, including time!
“A PICO-8 cart can access the current time of day, in the host system’s local time zone:
stat(90) -> year, e.g. 2018 stat(91) -> month of year, 1-12 stat(92) -> day of month, 1-31 stat(93) -> hour of day, 0-23 stat(94) -> minute of hour, 0-59 stat(95) -> second, 0-61 (usually 0-59, see note below) A corresponding set of values, but in UTC time, are available at stat(80) through stat(85).” - https://pico-8.fandom.com/wiki/Stat (PICO-8 Wikia)
Additionally, getting week day uses special formula you can find on my Twitter somewhere!