I to had this issue and it irritated the hell out of me.
I did a bit of googling and found some one who had the same issue on a shimano shifter but from a different group set.
They took it to there lbs who applied a little grease to a washer inside the shifter.
I decided to have a go at sorting it after my ride ride the other morning. It was very fiddly to get the shifter apart. But I did manage to succeed. I will try to describe how I fixed but I would look for a better guide on dismantling the shifter, I did find some instructions online but can't find them now.
- Shift on to the smallest ring
- Pull back the rubber hood
- Unscrew the small screw
- Pull the lever as if you are braking and shift at the same time and the front plastic cover will come off. A small piece of plastic and the metal washer will probably fall off.
- The washer is the cause of the buzzing. Look in side the plastic cover and you will see where the washer is designed to fit.
- Pop a little dab of grease on the washer and pop it in the plastic hood. Its a bit tight in there and the washer must sit correctly. I used a magnetic screw driver to get it in as my fingers were a little fat.
- The fiddly bit, getting it all back together.
- You need to get the plastic hood back on to the main unit making sure the washer does not move and get the small piece of plastic that came out back where it belongs. I used the other shifter for reference.
- Once its all back together pop the little screw back in and pull the hood back.
- Enjoy a buzz free ride
I some how managed to break the small plastic cover that covers the gear indicator. Not sure how. It still sits snugly but is now very easy to pry off.
I don't have much confidence in my technical abilities so if you plan to attempt this look for a more detailed guide about dismantling the shifter.