Yes, you’re right about that. I was making some confusion with the 737’s MCP, on which a green light goes on, when you switch the autothrottle button to the ON position.
As for the TOGA, I was trying to replicate the procedure I do when I take off in the PMDG 777 on FSX. At take-off I turn autothrottle switch on, I move the thrust lever on the joystick to 40-50% of its course and shortly afterwards I press the button on the joystick, which I previously mapped to the TOGA function. The system then applies appropriate thrust for take-off (defined in the FMC) and deactivates the thrust lever on the joystick, since the thrust is now being controlled by the autopilot.
Unfortunatelly I was not able, so far, to replicate this on FS2020.