I assume Eldritch Invocations are detected as magic, because they are magic:
In your study of occult lore, you have unearthed eldritch invocations, fragments of forbidden knowledge that imbue you with an abiding magical ability.
And Detect Magic spell detects magic like this:
For the duration, you sense the presence of magic within 30 feet of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
What does Detect Magic reveal about a visible warlock with Devil's Sight?
I guess there are two cases: the warlock actually "seeing normally in darkness" with the invocation benefit active, and the warlock being in bright light and invocation not doing anything. Let's leave the murky details of Devil's sight interaction with dim light and the warlock having or not having darkvision out of scope.