Sometimes my leopard geckos get swollen hemipenes (which is what looks like the "ball", but it's a hemipenis, not a testicle) and it turns out to be a sperm plug. When this happens I squeeze the bulge gently to evert the penis and usually there is a white thing hanging from it that can be gently removed. I don't know if your giant day gecko will let you handle it. If not, you could try soaking it in a warm "sauna". If you actually see tissue poking out of the vent, that is a prolapsed penis and he will need a reptile vet visit.
Aliza
