I think you have kind of already answered your own question.   But just to make sure...... The Brown/White ties to the Brown, and the Black/White ties to the Black.   They become your Neutral and Hot leads.   They tie together for 120 volts.   That is the important question.   Is Your Mains 120 Volts??   If so, then proceed.   Wire it just like in Nik's layout.
Hot from the wall goes to center of fuse, out the side of fuse, and over to the top of switch.   Center of switch goes to 120 of transformer and also over to pilot light.
Neutral fro the wall goes to top of switch.   Center of switch goes to Zero line of transformer, and also jumps to pilot light.
As you say, the Purple/White is not used.   Coil it up with a tie wrap.   Cover the end of that wire with shrink tube or electrical tape.   Even if you think there is no exposed copper, Cover It Anyway!!!
Because that transformer sees duty for more than just 120, there are some extra wires to deal with.   Just follow the Westlabs instructions.    Once you have the wires twisted together, consider them one wire.   Does that make sense to you?

I would wire it just like Nik shows on the Layout.    Don't let the DPDT switch confuse you.   It is two separate switches side by side.   If your amp came with the fuse wired to the center position, then the Transformer/PL would need to go to the top or bottom.    It does not really matter, just so long as you keep the Hot (fuse) lead on the opposite side of the switch from the Neutral (0 transformer line) lead.   The Hot and Neutral should only meet via the transformer, not via any other connection such as a , switch, resistor, fuse, etc. etc.
Just imagine the electron flow coming from the wall, into the AC cable, into the fuse, into the switch, into the transformer, through the transformer, into the Neutral Lead (and whatever it might be connected to) back into the AC cable, and then back into the wall from where the electrons came.
In the midst of all this electron flow, the Primary of the transformer gets energized.   Then from mutual induction, the secondary is energized, and that gives you all of your High Voltage 290V x 2, 3.15V x 2, and the 5 volts for the rectifier tube.
Now that I have over explained everything, do you have a digital meter?   If so, you can teach yourself how that switch works in 2 minutes.
Good Luck