I think you've got this all wrong; he's not making any mistakes you are.
Belly bands should not be used as diapers on a 4 month old, they are for older males who aren't neutered and mark in the house. One of the reasons he's going on the carpet, may be because he thinks of the carpet as a pee pad, unless you cleaned all the spots with an enzyme cleaner, they will continue to return to the spot, and urinate again. It wired into their brains, and you can't stop this, you have to get rid of the protein that's causing the smell, and only an enzyme cleaner will do this. Natures Miracle, or Simple solutions make an enzyme cleaner.
It's good that you are taking him to the pad during the night, but he's still really young to understand, unless you have been very diligent in training, and most of us aren't. Joey wasn't pee pad trained until about 6 months, and we had wood floors and tile in parts of the house, and he had no problem going on the pad in those areas, but the carpeted areas were much more confusing for him. Cleaning those spots, and using washable pee pads really helped. I don't know why he liked the washable ones better, but I was able to get his pee scent on them, and wash them with regular detergent not an enzyme cleaner so the scent stays on them, and he started seeking those pads. At first I would put the pads where he had chosen to make a mistake, thoroughly spraying the carpet with the enzyme cleaner, and placing the pad on top, then later I placed the pads in the areas I wanted him to go, and he caught on quickly. Save those belly bands for when you visit others.