How do I pause contacts on a Sequence rather than removing them from the whole Sequence?

There are two ways to accomplish this. If you need to pause individual contacts on a Sequence you can go into the subscribers tab of the Sequence and select the contact. At that point the option to pause/resume that contact on the Sequence will appear.

The second way is to use a Task outcome or Rule step. You add either of these two steps to the Sequence, and when the Task outcome or Rule outcome fires, the the contact can be paused/resumed on the Sequence.

Keep in mind, contacts that are paused are treated as not being on the Sequence while they are paused. This means that the amount of time the contacts spends on the Sequence does not increase for the duration of the time they are paused.