You can't use the "12v center tap" for a pilot light. It isn't another voltage in that sense, but a tap in the middle of the secondary winding. Looking at the picture again, I'm assuming the white lead is the center tap. So you'd measure ~12vac between white and red #1and 12v between the white and red #2, and 24vac between red and red. (Again, I'm assuming the transformer is "24VCT" or some such nomenclature or "12v-0-12v"
You would use the center tap with two diodes to rectify 12v.
See this link:
http://www.engineeringslash.com/power-supply/full-wave-power-supply.html
High voltage tube power supplies e.g. use a center tap, that becomes the 0V reference, and the two outside wires go to the plates on the tube, just like the diodes in the example linked to above.
The Royer circuit isn't really like those above, more like a pair of half wave rectifiers put together, so you can use one transformer and get two voltages.
Download this tool, it will give you some visual guides:
http://www.duncanamps.com/psud2/index.html
I avoid point to point as a matter of personal preference, so I opted for the high voltage transformer and used the PCB's. You could also do the G7 trick of back to back transformers. I emailed you the G7 schematics. Take a look at that PSU and you'll see what I mean. (Note, that is based on European mains of 220-240, so you need to adjust accordingly.)
I also have a thread at homerecording.com on my royer mod. You need to have an account there to see the pictures though.
Shameless plug: I have a few transformers with 80v and 9v secondaries and 135v and 9v secondaries, specially wound for these circuits. They put out a bit higher then spec'd and the 80v will give net about 118v under a 100k load on the BigUgly psu board (with about a 300ohm resistor.) Let me know if you want one.