Hello again Matt,
Since you have decided to use the starter fitted, it might pay you to clean the contacts inside; I imagine they will have oxidized over the years of inactivity.
Switch construction is easy. Two screws release the cover and you will see the cluster of windings I described previously upright in front of you. Across that is a Bakelite bar with an adjuster on the left hand end to set the overload trip current.
With a piece of fine emery cloth folded to give two abrasive faces, slide that between the contacts and latch the switch on with the Bakelite bar to apply pressure to the chosen contacts. Do this to each in turn.
You will notice that the underside of the OFF button terminates in a simple Bakelite cone to push the latching bar upwards to release and break the switch operation.
That really is all the maintenance the switch needs and done at the time you rewire a supply and refresh the motor connections, it should perform happily for years to come.
Regards
Brian