I do think/hope that when an opening date is announced, it will push people over the line. I think it's apathy and a lack of urgency that's holding back the few, now that there is a "choice" of vaccine for most.
I do wonder if King Mark needs to come out and threaten lockdowns and masks, if we don't get to X% by the time the border opens. The court cases may force that hand.
Of course there's some who no matter what you say, won't be pushed. We had an interesting discussion at a family event yesterday as to whether people refusing the vaccine should be refused treatment if they end up hospitalised (if/when hospitals get overwhelmed).
The health report discussed the lack of prioritisation processes earlier in the week, if that interests you. But back to the topic I wonder if that might push some to get vaccinated.