Testing whether today is the second or fourth Saturday of the month
A few suggestions


collections.defaultdict


holidays = {}
for month in range(1, 13):
    holidays[month] = []
    ...



There is a module for dictionaries starting with a basic datatype

from collections import defaultdict
holidays = defaultdict(tuple)


Secondly you first init it as a list, and afterwards you make it a tuple this is odd. Pick one and stick with it
You don't have to calculate all the months only the specific month

Since you already know which month it is now, just calculate only the month you are interested in

To do this you would have to give the month as a second parameter

def second_fourth_saturday(year, month):
    cal = calendar.monthcalendar(year, month)
    ...

Don't Repeat Yourself


if cal[0][calendar.SATURDAY]:
    holidays[month] = (
        cal[1][calendar.SATURDAY],
        cal[3][calendar.SATURDAY]
    )
else:
    holidays[month] = (
        cal[2][calendar.SATURDAY],
        cal[4][calendar.SATURDAY]
    )



If you calculate the weeks beforehand you don't have to repeat yourself

second_fourth_saturday = (1, 3) if cal[0][calendar.SATURDAY] else (2, 4)

Return what is asked

Instead of return a dict of month with second/fourth saturdays, I think it would be more clear if the function returns a boolean value if the day is a second or fourth saturday


Code

from calendar import monthcalendar, SATURDAY
from datetime import datetime

def second_fourth_saturday(date):
    month_calender = monthcalendar(date.year, date.month)
    second_fourth_saturday = (1, 3) if month_calender[0][SATURDAY] else (2, 4)
    return any(date.day == month_calender[i][SATURDAY] for i in second_fourth_saturday)

if __name__ == "__main__":
    is_second_fourth_saturday = second_fourth_saturday(datetime.today())
    print("Enjoy" if is_second_fourth_saturday else "Start working")