The unclued lights, four of two words, individually or as a pair, are of a kind.
 

Across

11    After hint turned up, end of match had leftist outwitted (7)
12    Problem with French name turning page (6)
13    January not starting pleasant round island — likely to be soaked?  (9, three words)
14    Break-time first — that’s the general drift! (5)
16    Light-hearted joking when taking tea with F-Fawley (5)
19    Data emerged; half rejected.