The rule for the pronoun use after the comma

I am always confused whether I can leave the pronoun in or out after the comma.

Michael, Anthony, Scarlet, and Bill combed half the parking lot, but (do I need a pronoun they) couldn’t find the magician.

Is there a general rule on this? My tendency is to put "they" in this sentence. Other times I don't want to put a pronoun.

Solution 1:

If you keep the comma, you should use the "they"; if you delete the comma, you shouldn't use the "they." The reason for this is that when two clauses are joined by a coordinating conjunction (in this case "but"), two independent clauses (which the addition of the "they" creates) are separated by a comma. However, if it is a compound predicate (without the "they"), no comma is needed because one subject is being used for the two verbs.