It looks as if Gill's DFC was for his time on 84.
He was in command - as an Acting Sqn Ldr - from October '42 to September '44.
His DFC was Gazetted - still as an A/Sqn Ldr RAFVR - in November '44, in the same list as another A/Sqn Ldr RAFVR - one Neil Cameron of 258 Sqn (Spitfires at the time I think)
Like most wartime DFCs, there is no further detail published in the Gazette, but - given the timing - it would seem highly likely to refer to his 84 Sqn time. Indeed, the Gazette entry refers to him as 84 Sqn, although he handed over command - to one G R Plumb - in September '44. Did they give DFCs as end of tour BZs as they now do with OBEs?
Still looking, but one would need to go to TNA for more details methinks.
And I must - as a ukulele player - add my favourite piece of Arthur Gill trivia. In the 1938 George Formby film "It's in the Air", Gill was "stunt double" for Formby in the flying sequences..........