I wonder if you'll need to make a reservation even if you're just passing through? I like to take hwy 120 to cross the Sierra from the Bay Area on my way to 395 and Lone Pine.
Yes, you need a reservation to drive through 120 Tioga Pass.
https://www.nps.gov/yose/planyourvisit/conditions.htmhttps://www.nps.gov/yose/planyourvisit/conditions.htm