Me baffled too...
Only need a rectifier if making DC - OK I accept a saw may need to make DC - to light a laser guide-light perhaps...
My electronics training years ago tells me a Bridge Recitifier needs 4 connections - AC in where the diodes are opposite to one another and the two DC connections where the diodes match.... How it might operate with a wire missing I can't imagine...
Is anything written on the Rectifier?
The fact that it's connected to the switch is neither here no there - just assembly convenience - Anti-Spark capacitors are nearly always fixed to the switch that's why I guessed it may be a capacitor.
Continuing good luck with your other question...
Peccavi
October 2009