I haven't looked at h2seq for a while, but... I'm pretty sure you can't bind joystick buttons directly in H2seq. It only takes the keys listed, using the codes listed. I have no idea if those are standard codes or ASCII or what.
You don't need to redo anything yet. From right where you are now, the next step is to try binding the gear up/down keys in h2seq cfg file to actual keyboard keys, using the codes provided. Say DD and DB for "[" and "]" - simply because I can see those codes in your screenshot. So instead of JOY1_BUTTON13 and JOY1_BUTTON14, you put DD and DB. Leave everything else in M2emulator and the H2seq cfg file as it is.
Now double-click the H2seq program, and check the taskbar cion down the bottom right to make sure it's running. Hover the mouse over icons to find out what they are. If H2seq is there, open m2emulator, open a game, and test the "[" and "]" keys while driving to see if they work.
If that works up to now, and you want to use joystick buttons instead of [ and ], look into Joytokey to bind those buttons to input [ and ] for you. Or, if you're already using something like UCR you can just use that, but it's pretty nasty to get into. Joytokey is easier.