The '120 votes to auto-qualify for the run-off' ISN'T a rule under the electoral procedures. It's simply a statement of mathematics.
With 358 Conservative MPs, if one of the candidates gets 120 votes (which is fractionally more than a third of the electorate), it's mathematically impossible for two or more other candidates to exceed that number at the same time (since there are only 238 other votes to be allocated between them).
So while Rishi Sunak will know that he's into the final run-off if he gets 120 or more votes, the election procedure remains unchanged, which means that his name will remain on the ballot papers for the next round. So there won't be 120-odd 'spare' votes to be spread around, as suggested in Ichkeria's post.