One unclued light is the origin of the remaining unclued lights (three of two words), individually or as a pair.
 

Across

4    Stagnation’s the making of these adversaries (11)
11    It’s for refreshment in moderation — there’s no din (7)
12    Reptile from southern-most headland (6)
13    Nut lovers’ collection in Laurel’s birthplace (9)
14    King of England swapping old money in 37 (5)
16    Motionless, it can make the spirits appear (5)
19    Child beginning to trust stranger gets left imprisoned (7)
21    Note time on Orkney isle (4)
23    Sin from Bible — a run on diamonds (7)
24    Smile and phone, when cycling (4)
25    Corrupt police? Constable’s work...