Rule #20 is the first Rule of Part C (Rules 20-31). A thorough understanding of the lights and shapes is vital because they communicate the size, type, and direction of travel of vessels, all details we must know in order to apply the Steering and Sailing Rules in Part B.
This Rule seems fairly clear. First of all Rules 20-31 must be complied with in all weathers; in other words, all the time. The lights required in Part C must be exhibited at night or anytime when the visibility is restricted. Many vessels leave their lights on anytime they are underway: day or night, clear or foul. That is a practice that is hard to fault. Other lights may be on as well, as long as the can't be mistaken for the required lights, do not block or overpower the required lights, or interfere with the keeping of a proper lookout.
Required day shapes must be displayed during the day even when visibility is restricted.