Does anyone know the origin of the term " he/she has a monk on" In practice it is usually someone giving the silent treatment i.e not speaking, so perhaps this term results from the monk's vows of silence?
I'm sure you have provided the answer yourself. Monks are people who, by definition, live 'apart' from society by cutting themselves off in monasteries. Some orders, such as the Trappists, actually take vows of silence, as you say. As a result, 'having a monk on' means a refusal to communicate with others...ie sulking.