Many primary schools in the UK in the 1960s/1970s would have had 'milk monitors' - pupils whose job was to help distribute small servings of milk to their classmates. The milk distribution was an attempt to offset child malnutrition. The role continues to evoke strong feelings today. The Brit ex prime minister Rishi Sunak was described as a 'jumped up milk monitor' and when (in the 1970s) Margaret Thatcher as education secretary (minister) cancelled the school milk programme, she was reviled as 'Thatcher Thatcher Milk Snatcher'.
I was "computer monitor" (no pun!) for a year in the 1990s, when I was about 10.
I can't really remember the timing, but perhaps in the first half hour before lessons had started I would go to the classrooms of the 5-8 year olds, and if the teacher wanted I'd switch on the classroom computer and load the required program. (Maybe a different child did the 9-11 year olds' classrooms?)
It’s listed on that page as a synonym for toil or drudgery. So basically a chore is a fag. It seems like the definition you mention is likely the origin of today’s gay pejorative.
