First, ditch the tom thumb. You can't show in it, and it's a very confusing bit. It combines the pressure of a snaffle and a curb into one piece, which can actually cause the horse to throw his head higher with less than stellar hands.
For training I'd go back to the snaffle, because they have to be great at the snaffle before they can go to a low/medium port curb bit.
I start out by getting excellent lateral flexion. Pulling to the side, hold until the horse gives, and release. I do this from the ground in a halter, and then fifty million times in the saddle. I want my horse to flex with a pinky's amount of strength. This will teach the horse to give to the bit, and will also lower his headset.
Then you take a steady hold of the two reins (snaffle), and push the hind end into your hands. When the horse lowers or gives, you give back plenty of rein. Rinse and repeat. Be sure to give plenty of slack, when you move to the curb you want your horse to be super sensitive to the pressure of your hands so that you can be on a draped rein. Having heavy reins helps translate the pressure easier. You'll learn how to work split reins like a pro, pushing them to contact, and releasing them to drape.
If the horse balks up, I push into a quicker circle until he gives that dip. You also want to eventually be able to walk forward and flex laterally.
Just remember to be very sensitive and release, it will take some time, but the horse will eventually learn to be responsible for his own head. The process goes much easier if you supplement by doing lots of core-body exercises, like figure 8s, roll backs, half passes, side passes, pivots, and leg yields.