Sentence:  The ′40s and ′50s were in advance of the day of the twilight <WSD>double-header</WSD>, and most certainly before the more common twilight or “twinight” <WSD>double-headers</WSD>, in which the fans must leave so as to empty their seats for a new crowd which is to see the second game at a separately scheduled time. 
Meaning of the word marked with <WSD> tags:  A pair of games played one after another between the same teams.