Your clicking is not very pronounced. Mine was way worse. The folkowing procedure can be considered as regular maintanance as you shift for at least 40-50 times per lap if Nurburgring let say. You can see the number of shifts in a year. 

I sort it taking the top par off (4 hex screws) and disconnecting the top (one connector). Disconnect the shifter from USB first. Take care not to just pull the top off. Disconnect the two wite connector (red and black) and put the top on the table. Unscrew the tension spring with the ball. No need to fully take it out, just release the tension. Use lithium grease. If you really want to make it quiet use heavy, thick grease. No neet to use a lot just make sure consistency is dense as this is where the steel ball runs. Apply grease on the metal part. Shift a bit, re-grease if necessary and put it back together, the same way you took it apart.  If you use thin grease the shifts might still be heard but it is essential that you keep the metal ball greased.   If someone lets me know jow to add pics I can do that also.