Same here, the automation doesn't seem to work at all, don't think I have the stomach to click to 10 billion lamps... Fun little game though!
Ah, I see. If you ignore lampy on day 1 when he tries to unlock it, the conversation is still available later but it does not enable the automation. I suppose 2 things need fixing there, make the activation more obvious (currently it spams his switch on/off SFX and pops an exclamation mark above his head, but with low/no audio it's totally missable) and make sure it always works regardless of when you have the conversation with him/just force it on if you don't do it on day 1.
Thanks for letting me know!