Build on what Marsha was saying by making him work. If he's jigging while working in hand - (say leading while at a walk) - immediately switch directions - hard left and using that whip to cue him right back up to your side. Or turn into him - making him move away from you smartly and keep going. Do this from both sides. Don't "pitty pat" around - step out. If he's a smaller mini, he will either need to stretch his legs to flat walk or move into a nice trot to keep up with you. Use your own "gait" faster to move him at more than a "jig". But if he jigs instead, like I said, immediately switch directions. You may start out by switching directions every couple of strides(your strides). That's ok.
Is he jigging in different areas or jigging always in the same area? If it's the same area, utilize that spot as a hard work spot. U wanna jig? He needs to understand that if he does that very undesirable jig, there is hard, sweat making work to do. When he's huffing and puffing, offer to slow down and ease up. If he jigs, go again. You will condition up too, I promise, LOL. Then take him back to a spot that you use as a reward spot and give him a few minutes to "blow" and get his air back. Then start out again.
This can be done in hand first and as he gets better about both jigging and standing still, you can graduate to ground driving. He can be ground driven in circles and figure 8s so that he's working while you are essentially standing still. Again lots of changes of directions (it will help you to gain control of the lines, too). It doesn't have to be pretty at first (though you do want to be careful you aren't snatching/grabbing at his mouth with the lines), but it will all come together. If it's easier for you, set up obstacles to drive to or around. I often use the plastic laundry jugs or 2 ltr soda bottles (did a lot of laundry and drink loads of soda). Or you can use boards, rocks, cement bricks, tires. Imagination is good! work him in hand uphill, downhill, thru ditches along your driveway, along the road. While leading, teach him to go ahead of you and cross over in front of you, turn towards you and turn/face the direction you are going. then to go from one side to the other - he will eventually slow down the jigging OR will just become really really fit and may not make a driving horse.
Then once you seem to have a handle on the jigging, go to working him with shafts. We used pvc pipe. The old, tried and true driving book by Doris Ganton recommends wood. We started with one pipe on one side, then switched sides then went to two, etc. The pipes were left loose on the end on the ground and later, they were hooked together. We did/do a lot of tire dragging. We drag brush and "log" trees. Work him regularly and he will realize that he doesn't have to work so hard by jigging.
This is not a one time thing. Depending on how long he was jigging, it could take months or even well over a year to finally fix. My "squeaky wheel" mare, also a jigger, jigged off and on no matter how much work she got BUT we kept on. When I was able and did keep up with the constant switches in directions AND speeds, she became better. When trail driving in a long shafted cart with a large group of drivers and riders that's hard to do - she spent one trail drive on her hind legs most of the day. SHE WAS TIRED by the end of the drive, though. I worked her pretty hard at home the next day and suddenly she didn't want to jig so much... She did get bathed and her legs got rubbed with liniment. She did not get fed right away when we got home from the group trail drive.
Also, incorporate a "tie-time" or "patience pole" - where he stands tied a couple of times during the days that you are home and around. Make sure that he spends time tied up between his work out and being fed. Just because he's hot, tired and sweaty doesn't mean that he is automatically and right then get washed, groomed, fed & turned back out to pasture or put up in his stall (within reason, of course, if it's a miserable day, then you can change that up). This is the type of horse that will benefit from things not always being done at the same time or even in the same way every day, again w/i reason...
When growing up with riding horses being started under saddle (on weekends & summer holidays), I often led the youngster(s - 2 - 6 at a time) out to the round pen saddled, girths only tight enough to keep a saddle on, not step into the stirrup and ride off(before they were even fed). Then I'd have to do some chore or other for a bit. 1 or 2 would be led into the barn or a bucket would be hung in front of them w/ their breakfast where they were tied. When finished they were taken back out to stand tied or the bucket was removed from their spot. None were fed at exactly the same time. If they started pawing, or getting antsy, their feed was held back or even skipped at that time (I never had major pawers until we got into the Shetlands, OMG. I've tried every trick I know and consulted with many others and still have CONFIRMED pawers that don't quit). At noon(ish), before I went into my own lunch, each horse was untied from the round pen and led to the water tank. didn't take long and they learned that they probably should drink - it often became quite a long afternoon. If we had some that we knew were antsy or would paw - and they were displaying that tendency and then quit - they were led into the barn and unsaddled and put up - whether in a stall or turned out in pasture. In between chores or whatever we might be working on (& sometimes mom, sister or a couple of neighbor kids joined in the riding), might lead one into the round pen and tighten girth then get off and on a few times, loosen girth and lead back out to tie up. Then might take another, mature horse loose from tie spot, tighten girth, swing up & ride/work them for a bit outside the round pen - swinging a rope, backing up, trotting, loping & galloping around the others tied up to the fence. Then step down, loosen girth & tie them back up and go do something else. We had some very "broke" horses and lots of folks clamoring for us to work with theirs... Took them to shows & rodeos - though most often we weren't showing ourselves. Just had them stand tied at the trailer, in a stall in the barn or led/worked them on the grounds.
I incorporated this with our young riding and later with driving ponies (both babies and old broodmares just learning to drive). It WORKS!
One of the things I did one summer when I had 3 young ponies to work with on ground driving and wasn't doing enough with them - I started swapping back & forth working 1 or the other while they were eating. Sometimes, I'd slip a bridle on their head and ground drive them, sometimes just a halter & lead. I didn't groom them, didn't harness them. They got taken away from their feed bucket for 5 -10 minutes at a time. They drove away from the feed area out of the barn doors and up the incline behind the barn. halt. Turn this way, turn and walk away from the water tank. Drive to the barn door and thru it right past their feed bucket and continue thru the barn out the other set of doors. Halt, back into the barn. Turn back towards bucket, back out of barn & turn different direction and walk off. figure 8, back thru the barn door, past their bucket and out the other door, halt and back all the way to their feed bucket. Stop, undo lines and hook them back up to their spot... Then switch and do the 2nd one. Then switch and do the 3rd. I usually always worked one longer then the next and the last one the shortest amount of time as I realized that I needed to get other stuff done. The next day, they'd get swapped around as to who got worked first/longest. I tried to never work them the same time each day. This worked as well. They learned that I knew they had to eat and that while they were away from their own bucket, no one else got to it (everyone tied up). They all learned that they did get the chance to eat - food didn't need to be "bolted". And all 3 became quite nice driving ponies...Often times, I spent NO MORE THEN 15 minutes TOTAL between the 3 every evening and no longer than 30 minutes. Those were some of the best spent "driving" time those ponies had - and it worked on the old, confirmed, spooky jigging mare as well when she was incorporated into the "mix"...