Does he attend any toddler groups, nursery etc? Does he meet any other children, and if/when he does how does he react with them?
Who else is in the household, Dad, siblings? Do you have any pets; does he play in a garden? What toys, games, activities does he have at home, and what sort of play does he prefer? What TV, radio does he see/hear, and does he have other screen-based 'tech'?
Sorry for all the questions, but I was a TA/helper in primary schools for twenty-five years, and I invariably feel there is an reason or cause for a child's behaviour or attitude, if only one can discover it - which, obviously, can be extremely difficult.
Are these periods of two weeks 'all right', then a transition period, then 2-3 weeks of 'devil' REALLY as clear cut, and consistent, as you say? Can you keep an ACCURATE record of the exact periods of time, and the corresponding behaviours, as I am wondering if you should make your GP aware of the situation, if there is no other explanation that MNers can come up with.