I can only talk about the server I play on: Moogle.

Between 4PM ~ 11PM GMT is the most active period during the week (it's different on Saturday/Sunday).

I don't know where you are so I don't know what is "2-5 am" for you, but if it is about GMT, then it's also deserted on Moogle. During that period the Party finder is usually empty or at best 1 or 2 group recruiting for Khloe or some Raid.

Also since the release of Final Fantasy XV, it's even more deserted xD