Skelhon scored 693.2 in total to finish third in the mixed event, a discipline he only took up 18 months ago.
And he only missed silver by 1.4 after just scraping into the eight-strong final in seventh place from the earlier qualifying round.
Skelhon, who won silver earlier in the Games, cut a striking figure four years ago when he won gold in Beijing wearing a bright Mohican haircut.
Now sporting a more conventional style, he couldn’t find the words to express his surprise at pulling off a second medal-winning performance.
“I am speechless,” he said. “I can’t actually believe it at the minute. It’s amazing.
"I came here to win the prone and came away with a silver but I shot personal best and it was a phenomenal competition.
"Now I have got another medal and I'm over the moon with today and dead chuffed to get two medals.
"The first ten shots I messed up and then I gave myself a talking to. I had a couple of shots that I messed up and without them I could have got to the finals in a more comfortable position.
"In the final I didn’t look at the scores until half way through. I knew that I was back in seventh at the start and I just wanted to focus on my own shooting.
“I heard all the cheers so I knew I must be doing well and when I looked I saw I was in third.
“I’m never going to be disappointed with that. No one should be disappointed at the Paralympics."