Curate, connect, and discover
Danny wears sunglasses 24/7.
So much so that slowly it's been ingrained into everyone's minds that he's never taken them off. Like, they can't even remember a time where he hasn't worn sunglasses.
It's just like, his thing.
Why does he wear them? Well, because Danny's previous blue eyes changed to a startling, glowing green that he knows the GIW would eat up and use as a reason to force him into their custody.
Solution?
Sunglasses.
His parents? Oh yea they went all in when he they found out why he was wearing them (Reveal gone right au babyy). They made them extremely durable; they can film audio, take pictures, take videos, see through walls and even track down ecto-signatures for whenever he's tracking down a ghost in human form, see through walls and self-cleaning.
(The ectoplasm tracking system is for when they aren't close enough to set off his ghost sense.)
He honestly believes his parents watched a spy movie before they built him these, but it's not like he's going to complain about it. The only time he isn't wearing them is when he goes ghost, you know as a way to not link him to Fenton or whatever.
So, Danny meets John Constantine while the both of them were on the hunt for a ghost who was causing problems in the area. Danny manages to find them first, the ghost in question being an animal who was terrorizing a place because it didn't understand the fact it was dead yet and wanted to protect it's children.
John Constantine comes while Danny is pacifying it. He watches as Danny calms it down enough to get to the babies and sends it to the Ghost Zone after promising it to get them somewhere safe.
John Constantine also saw his eyes, because he pulled his sunglasses off to show them to the ghost as a silent sign to trust him. John Constantine of course asked what he was going to do with the babies, and Danny just sent them over to Sam.
After that he decided to keep an eye on Danny because of his eyes. Which were the eyes of a ghost, and he was genuinely thinking Danny was possessed before that went out the window. So he thinks Danny is a ghost pretending to be human and wasn't able to hide his eyes so he wore sunglasses.
Danny neither confirm nor deny that.
So Danny just kinda followed him around until Constatine eventually made him into a contact whenever he was dealing with ghosts that he could peacefully deal with instead of just forcefully banishing them to the Infinite Realms.
This, eventually, comes to light when Constantine goes "I know a guy." In front of the whole Justice League, bonus points if they somehow come to the conclusion that Danny is Constantine's secret child, sidekick or both.