You can start jumping on the lunge or (better still) in the round pen, with ground poles....these will make him look down, lowering his head and automatically bringing his back muscles into play.
This should be enough to start with, even at 10 (Yay for the mature geldings getting a job, BTW!!) as if his muscles are "immature" you will need to go easy, in fact you will need to go far easier than you would with a younger horse, as he, and his body, will have become set in his ways!!
So stick to ground poles for at least a week or so, and introduce them slowly, one at a time.
When you think he is ready put the middle one (I use five) up on low blocks and then slowly progress until every other one is up on a low block (six inches).
After that you can take out the remaining ground poles and put the last pole up to double height (you are now at one foot and there is no need to go any higher, a horse that will readily jump one foot for fun will jump any height you put him at, that he believes he can clear!!)
Once he is jumping freely an if he looks as if he is enjoying it you can start putting in different sorts of jumps (there are a couple of web pages that give instructions, I think, and Dog Agility fences also work)
If you have come this far on the lunge and are athletic you can progress very naturally to jumping in hand, as the horse will be focused not on following you, as they tend to be if you teach them to jump in hand, but on the jump.
He will also have learned to work out for himself where to go and when to take off.
You can also try long reining him up and down and "bumpy" ground you can find, he will, I think, enjoy that too.
It is also good training for future driving, which I really do hope is where you are heading because you just cannot find a better way of engaging and strengthening the rear end of the horse than a
correctly trained driving horse!!!
Good Luck