Red-faced city election officials held an apparently illegal, secret meeting Wednesday to discuss the botched vote count that threw the Democratic mayoral primary into chaos, The Post has learned. Board of Elections President Fred Umane said the board was briefed by staffers about the colossal screw-up that led to 135,000 fake ballots from a test run of the BOE’s computer system mistakenly being included in preliminary results released Tuesday afternoon. Umane, a Manhattan Republican, said that the test ballots came from one borough but that “the error was made in the general office.” “We’re still trying to do the investigation....