I think that one refers to doing so when there is no food on the chopsticks. Picture tapping the chopsticks against your lips to show you’re thinking, if conversing while eating. The overarching rule being that you should put the chopsticks down whenever you’re not in the middle of picking up/moving food with them.

(Unless you want to come off as imitating a Rakugo storyteller. If you do, then go ahead and use them as a talking prop. But maybe make it clear that you’re not eating with those ones, so people don’t worry you’ll flick sauce at them!)