Remove the speaker covers (they are just glued) and the top rubber caps and then remove the underneath screws.

Open the round case with a credit card, your nails or just something soft to avoid damaging the case

Remove the screws, but don't remove the PCB from where it's sitting, we just need to lift it a little bit from the left to put our PCB bellow.

Remove the components highlighted in yellow.
The connection points for the mod are highlighted in red

Prepare a PCB with the following wiring.

The pinout is compatible with microchip ICSP, so, it can be flashed even after soldering.

Solder the wires to the PSONE PCB.

3V

GND

CSYNC (microcontroller input for detecting the type of signal)

PAL / NOT_NTSC (output to select the timing)

And solder the female header on the other side.

I just left 2 spare wires for future uses.

(The rigid wire at the left was just for testing purposes)

Flash the microcontroller with the provided hex file.

Put the PCB bellow as shown:

With this orientation, you will see that there is no need for insulation, but feel free to add some insulating tape or heat-shrink tube to the PCB.

Now you can tighten the four screws to secure the PSONE PCB.

Route the wires as shown and you should be able to put the case back without forcing anything.

This is the expected result:

PAL boot screen:

NTSC game: