I take the opposite view to you in that I think that those who didn't vote, would have actually voted to leave, so it's actually 70%+ in favour of leaving. However, we will never know what the absent voters would have chosen, so we can't sensibly count them. That leaves us with the leave majority which is all to familiar to pro-remain.See, you would think the job is now to convince the 70+% of the country that didn't vote for this, that it is a good idea. Not sit back, be smug and think you've done the job. Its not complete... complete is making a success of it!! Delivering on the promises made.
If you / they can't convince people that this is a good plan, the influence is very much still intact. We've not left until we've left, and even once we've left we can simply apply to rejoin. So if you want to be out of the EU, the "leavers" do need to win some arguments, because if you keep loosing them, or hiding from them, your dream will fall apart before it even happens.
I don't perceive a requirement to convince anyone. You can either get behind BREXIT and give it every chance of success, or you can stand on the sidelines sporting a mardy lip and pulling the wings off flies.