Instructor in Gunnery/Assistant Instructor in Gunnery/Master Gunner White Hat

My first post, be nice........

I think this venue may probably be the best place to ask for this information.
I am currently serving in the Royal Canadian Artillery School (RCAS) as an Assistant Instructor in Gunnery (AIG). The topic of discussion here which has caused a much heated debate is the origin of the UK/Canadian AIG/IG hat. Why it is worn, where did it all begin and where it started, and who ordered it. What is the signifigance of the white for the Technical expert and not for the Officer?
Only speculation and unsubstantiated theories are present, here at the RCAS(from some very senior Artillery staff) and none can be backed up with historical reference and/or fact. The old plaque on the wall is somewhat inaccurate and, I have been tasked to investigate this problem to hopefully put an end to the constant debate.
I feel this is the best venue to ask to provide a factual answer.
The attachment below somewhat explains some personal opinions, but not facts.
The AIG(White Cover) worn by the NCO, and IG(Khaki Cap with brass capbadge) worn by the Officer, hats are worn today.

Any information you could provide to me would be greatly appreciated.

Thank you for your time and patience in this matter.