As an ambidextrous person, how do you switch between writing with your left and right hand depending on what you're doing or where you're sitting?

There is no switching going on, there is just convenience. Whatever is convenient you just do. It just happens.

If you can only use one hand well you have no choices. You have to arrange or organize yourself to do the task in the way you can do it.

If you are ambidextrous you let other factors determine how you accomplish the task that have nothing to do with your limited dexterity.

For example when I was a teacher I would start with my right hand on the left side of the whiteboard. Eventually I would hit the middle of the board and switch to my left hand as I crossed to the right side of the board.

I did this because I prioritized the students being able to see me write over using a single hand. My back was always to one side of the board and my writing was always viewable to the majority of the class.

The determining factor for this practice was not the limits of my physical capabilities, it was the effectiveness of my teaching.

Hope this helps.