Smoke
Ignore-Amus
If you note in your photo - you didn't cut to two buds - you cut to three. The key is to let the new growth push, unrestrained, harden, and then you cut back back hard - two leaves on weak growth and one leaf on strong growth - and no leaves on a long shoot with too long internodes.
From a horticultural perspective think of it this way - you let the tree grow and bulk up with energy, and then you cut back hard and remove the source of auxin (branch tips) that suppress bud development. If you cut back too early and there is no stored energy - no new buds. If you wimp out and don't cut back hard enough and don't eliminate enough sources of auxin - no new buds.
This really pains me. It is auxin, not 'energy'. There is lots of auxin generated in elongating tissues, but it isn't being exported down the stem. Therefore, when one cuts soft, unhardened stems, it has little or no effect. Once hardened, auxin is being exported. Then lopping off the auxin produces releases bud(s) --> Thiman=Skoog, nearly 100 years ago now.
Just gravitropism reduces the auxin flow enough to release interior elm buds.
Wire your shoot and bend the tip down. Position the node where you want a new branch to be at, or near, the top of the arc. Wait a week or two. It is just like 'pegging' roses.
The other part is that soft, unhardened tissues are consuming more carbohydrate than they produce. So, removing it does just reduce carbon in either case. But hardened foliage allowed to remain exports lots of carbohydrate - thus feeds the rest of the tree. Feed your tree for a while by keeping the hardened new growth for a while if you want to build its strength (opp. if you want to weaken it).
Interesting, I don't partake of this method at all. This method is a branch ramification nightmare here.