I would set both due dates and available dates for each section, setting the available date to close at the end of your class periods for each section.
The problem with leaving the quiz open is that a student who is absent or perhaps has an extension would be able to take the quiz anytime. So, for example, and absent student could take the test at home after talking/texting with friends who took it. You would see the time stamp, but still it would cause an issue you don't want to deal with.
To deal with second attempts and absent students, you can also assign students individually with specific due dates, just like you would a section. So if a student is absent and they are going to take the quiz at a later date, you would just need to set that due date an available date. For retakes, give them the extra attempts and then same thing,
It actually works very simply once you get the hang of it.
See: How do I assign an assignment to an individual stu... - Instructure Community (canvaslms.com)
And make sure you understand the difference between due dates and available dates. What is the difference between assignment due date... - Instructure Community (canvaslms.com)
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