I've only ever heard about issues with a dead sounding bass drum tree mounted 12" tom. Not the 10. Not the13. Not the 12 as the high tom like in a 4 piece. Just the 12 in the 2nd position.
Happened to me too. Below isn't a popular opinion but it's the only thing that seems plausible to me.
Try this just for fun. Mount it, sit behind the kit and hit it. It should be dead right, the reason for the thread. Now move your head closer to the drum and hit it. Now move your head a little further from where you normally keep your head and hit the 12" drum. Now move your head back to how you normally keep it and hit it. Did you hear a difference? I do, bigtime. When I move my head closer to the 12" tom, it regains it's fullness. When I move it farther away from normal, it regains it's fullness. When I keep my head where I normally keep it, it sounds hollow.
My theory, and I don't know if it's right, is that my ears, where I normally keep them while playing, are sitting smack at the bottom of the trough in the soundwave. When I move my head anywhere else but normal, there's no problem. Try this, walk out in front of the kit and hit the 12" tom. Does it sound dead from out there? If it doesn't sound dead from the front of the kit...it's not. The only place where it sounded dead to me was from the throne with my head kept where I normally keep it. I think of it like a bad place to put a mic. Also no one but me is perceiving it.. I contend that the 12" tom is just the right size, and makes just the right wavelength, for this phenomena to occur.
If you are not suspension mounted, that could also do it. I'm a big fan of suspension mounts because I like sustain. The combination of the 2 could be your issue.
The other "problem" could very well be an ear placement issue. That's my theory. Until actual facts explain what's happening, I'm sticking with this.