Japanese uses ‘go’ (and ‘come’) as auxiliary verbs to convey change along a timeline, said to be aspect, but not to mark future. English ‘go’ does have some uses that parallel the Japanese use as auxiliary verb.
‘come’ when metaphorically the change brings something closer. ‘go’ when the change distances something.
Distant and close relationships are conceptualized as spatial. In Japanese and English. But also in Japanese and English, lights going out can be thought of in terms of distance. Lights can go out and come on (not come in.)
Candles can go out, but not ‘come on’ or ‘come in’.
‘go extinguishing’ means an extinguishing change happens over a timeline. And the result is felt to be further away.
‘Go out’: The result of the candle going out is not a ‘welcomed with open arms’ result. It feels foreign. In English, feelings about ‘go out’, ‘go off’? The default state is ‘on’ or ‘in’?
In English ‘become’ is more the default way of conceptualizing change over a timeline than ‘go’, I think.
In English, ‘come’ for change from past to present, and ‘go’ for change from present to future.
push comes to shove — Phrase: 1. (figuratively, idiomatic) When the pressure is on; when the situation is critical or urgent; when the time has come for action, even if it is difficult. https://en.wiktionary.org/wiki/when_push_comes_to_shove
In a power outage, the lights ‘go out’ rather than ‘come out’. When power is restored, do the lights ‘go on’ or ‘come on?’
I think both are possible, but ‘come on’ is more usual than ‘go on’. If you’re waiting for the lights to come on, they ‘come on’.
If you’re not waiting, or you expect them to go out again soon, it might be, “Ooh, the lights have gone on again.”
Lots of British National Corpus hits for ‘lights go out’, none for ‘lights come out’
One British National Corpus hit for ‘lights to come on’:
High on the wall of my room, near the open window,
waiting for the lights to come on, a gecko is
clinging on hopefully to the knobbly plaster.
None for ‘lights to go on’
From PBS 2014, via COCA: Corpus_of_Contemporary_American_English
... like the elephant in the room, but all the
lights are off. So you're feeling around, and you're
feeling this quite huge thing. And it was just - it
was an amazing relief for the *lights to go on*.
TERRY-GROSS# So when your parent came out as a
trans-woman, ..
Car mag, Mashable, 2016, via COCA
... the Bolt's Bluetooth system automatically pairs
with the phone. This causes the *lights to come on*,
making finding the car in a dark parking lot ..
The 13 COCA hits for ‘waiting for the lights’ have
But no ‘waiting for the lights to go on’.
So, ‘come on’ because like Japanese, ‘come’ is used for a result that feels familiar or preferred and not ‘go’, because that is used for results that are dispreferred or, in some way, ‘out’.