New user. I had the same problem but found the SOLUTION.
Settings>Display>Edge screen>Tap EDGE LIGHTING>Tap MANAGE NOTIFICATIONS> Move slider to ON.
Also if you haven't already, download EDGE LIGHTING PLUS from Galaxy App store for more customizable options.
This worked for me. I had only selected on for my Samsung Messages app along with my Google Messages app with the rest not selected. But your tip worked perfectly. lol
Good news is, they just released an update for the Samsung messages app in the Galaxy Apps store and it fixed this bug. Trust me, it was driving me crazy not getting pop ups. I woke up one morning and the messages app had an update available. Poof, Edge Lighting started working again.
I own a Note9 and it is up to date with updates. My issue with Edge Lighting is different and just started, as far as I can tell, in the recent past. (Today is 4 Nov 2018.)
I have Edge Panels and Edge Lighting _turned off_ and yet I still see the Edge Lighting effect.
If I open Settings abd just click on Display, the Edge Lighting comes on and blinks twice rapidly in succession.
I am at a loss on how to turn this off. It also flashes on other occassions but I am tried of wasting my time on this. I wish Samsung would sort this out.
I have the same problem. Only time edge lighting works when screen is off is for a text message. Doesn't work for Skype or What's App. Only works for what's App if you turn on pop up notifications.