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I'm not sure that's feasible because the brake lever isn't stopped by the top of it coming to rest up against the plastic lever body. Instead the part of the lever behind its pivot actually comes to rest down on the body of the main casting close to where the securing bolt is. The plastic housing doesn't really have a surface to glue anything to and I'm concerned about anything I put in there falling out into the lever, which sounds very sub-optimal.
Glue a bit of plastic, or cork or something, in the gap between lever and body.