Is really that "Breath Stops when Thought Stops" Is Body - Breath - Mind are connected to each other, and Thinking process really need oxygen to operate. When I sit for meditation i feel my breath is stop (Gap) and thought slows down, but for very minimum time.
Mental Fabrications is associated with sensations, hence will not stop until sensations stop. There are ways to stop thoughts is to develop Nirodha Samapatti or realise Nirvana by other means. When you have Nirvana as object only will your thinking stop. Verbal fabrication which is Thinking and Pondering will stop in the second Jhana.

When breathing stops your bodily fabrications have stopped. But when thoughts arise new fabrications arise which might have bodily impact hence breathing start again.

The there is a gap or breathing stops you have to contemplate the sensations you experience in the upper lip or even the whole body. See: LECTURE FOUR: MASTERING THE VEDANA by ANAPANASATI - MINDFULNESS WITH BREATHING Unveiling the Secrets of Life: a Manual for Serious Beginners. When the breath is there look at the flow and touch of the breath. When it is not the sensations on the last point the breath touched. (2nd Tetrads)

Do not get alarmed if your breath stops for a long duration but this should not be forced.



Source: Anapanasati