Hmmm, usually silicone is not nearly as slippery as mineral oil/lithium grease like that at http://www.cyclesuk.com/337-518016
The silicone stuff is usually better reserved for contact corrosion protection and to keep rubber from sticking. It might be good for plastics, for example if the microswitch plastic shafts bind, or for plastic gears (provided that the particular formulation is compatible with the plastics). But for metal to metal mechanisms I'd recommend regular lithium grease (need not be white, but no moly, no extreme pressure additives) used sparingly (which means apply some with a clean screwdriver tip, work the mechanism some, then wipe off the excess grease at other than the friction areas). Since grease acts as a dust magnet, best to have it exposed only where it is really needed.
It's really important to clean out the old gunk first before applying new grease, and sometimes this requires mechanically chipping crud away if solvents do not cut it!