Litter Trained during the day, but not at night?

Its ben a month since I'm trying to swap from bedding to fleece, not fleece liners, just covering the bottom of the cage with fleece, but have a litter box.
Untill he is properly litter trained he is barebottom in case he has "accidents" and if he starts peeing on fleece, he might just start peeing on everything fleece. Maybe? I hope not.
The thing is, I only find urine outside the litterbox in the morning. The rest of the day, he goes inside the litterbox and pees there.
Its only when Im sleeping he rebels.

Now here is the tricky part, he doesnt just pee on a "night corner" he pees anywhere on the bottom part of the cage.
In any of the 3 corners as wel as the middle. I cannot predict where he is gonna pee at night, but again, he only pees in his litterbox when Im awake it seems.

Everyday for the past 2 weeks Ive ben taking paper to clean it and leaving it inside the litterbox, cleaning the spot with vinegar.

Im considering getting him a second litterbox in the meantime, but I just dont know where to put it.

Anyone else with a similar experience?

Oh btw, he is 6 years old now, but I believe old dogs can learn new tricks.