Yes, Ceaser's behavior is a bit odd. However, I have seen roosters become curious about the nest boxes, and go into them and even sit for a while. My current rooster is four years old, and decided a few months ago, that he no longer wants any hens sitting too close to him on the perch. He would push them off the perch with his beak, so now there are dividers on each side of him. He was raised in a rooster pen, and had his own perch, in that coop, for almost two years. Now, he is enjoying his own space again, at night only of course. During the day he is a Romeo! Poor guy...come to think of it, maybe he's tired.
Your Ceaser may just like being alone in the nest box.
However, you are right to give him physical exam. Anytime there is a change in behavior, whether it is a hen or rooster, an exam is warranted. Just today, my rooster was in the garage, as he always does, but he was standing in the corner staring at the wall. I knew right off, this was not normal. So, I picked him up to check him over. He immediately made some gassy sounds! He was having a crop issue. I gave him some medicine, and two hours later, he was running around with the hens. It's always best for the chicken, when you catch an illness early.
God Bless
