I don't pause time on breaks in my exams (and the University does not ask for those in disability accommodations).
But I have added time in Classic Quizzes for a couple of situations outside the student's control.
In general, I do that by having some slack in the "Available Until" date, and restrict the time the students can access the quiz by setting a Time Limit.
This allows me to add more time to all students in the Moderate Page: Once I publish a (classic) quiz, how do I use the Moderate Quiz page?.
It does not pause the attempt, just giving extra time.
I am not as familiar with New Quizzes, but if it is a New Quiz, you can use the moderate page to manually submit the current attempt, and then reopen the quiz to the student:
How do I moderate a student's quiz attempt in New ... - Instructure Community - 655
Note that depending on grade and solution posting settings, the student could see the solutions between the closing and reopening of the quiz.