I've built the circuit on the PCB, and it works, but I saw that my transformer has a secondary of about 17Vac and one of about 12Vac. I connected the tap switcher to the 17V secondary.
I found the following 2 things: when I increase the voltage, when the relay goes ON, then the CC led of the PSU lights for a fraction of a second. The second thing that I saw is that when the output voltage is very close to 13V (the switch point voltage) then if I turn off the PSU, after 2-3 seconds, the relay goes ON then OFF, also the relay's led (I used a amber led).
Edit: and the relay is chattering when powering the 12V/35W light bulb and when I increase the output voltage.