12 days in Japan

Hi - I'm hoping you can help guide us if it's worth the money to purchase the JR Pass given our plans below OR if it's more economical to purchase everything separate.

We'll be in Japan for 12 days, but will be in Mt Fuji for 2 days out of 12 days.

Day 1: Narita Airport - Tokyo
Day 2: Tokyo
Day 3: Kawaguchiko - Mt Fuji (bus)
Day 4: Mt Fuji - Kawaguchiko (bus)
Day 5: Kawaguchiko - Osaka (bus, then shinkansen to Osaka)
Day 6: Osaka - Kyoto (shinkansen)
Day 7: Kyoto
Day 8: Kyoto
Day 9 : Kyoto - Tokyo (shinkansen)
Day 10: Tokyo
Day 11: Tokyo
Day 12: Tokyo - Narita Airport

If we buy the 7-days JR Pass, I think (if possible) to activate JR pass on Day 5 (to use shinkansen to Osaka from Kawaguchiko) then use pass again from Kyoto to Tokyo.

Is it possible to choose a day when the JR pass is active? OR it is automatically active the moment it's purchased picked-up (Day 1)?

Thank you!