After soldering about two or three wires to the terminals on the three-way switch I noticed that I fried the contact on one side of the switch. Based on my visual inspection it appeared that the switch was now reduced to a two-way switch.
Luckily in my parts inventory I had the original equipment 3 way switch made by Fender. This part seemed sturdier. At least it was able to withstand my soldering of the wires according to the supplied diagram. And that switch provides a 3 way function.
My complaint is that the supplied Allparts switch may be a cheaper substitute part. I would have hoped that the Allparts switch would be as good or better than the Fender switch.