Some time ago the tumbleweed badge description was changed from no votes to zero score. ( Tumbleweed wording is incorrect )
I think the criteria should have been changed instead. In a recent ELU meta post I got the badge after a week with +4/-4. ( Let's get rid of the "correction" tag ) It seems to me that such a question shouldn't merit a tumbleweed badge. That was more than a vote per day which is in no way something that should earn a pity badge.
Thus, I suggest to change the behavior of the badge to what it originally was and only award if there really were no votes.