My take on a brush gun is a bit different than some.
It's pretty much carved in stone...........bullets DO NOT deflect limbs. A 10 gauge slug makes, statistically, not much better of a "brush gun" than a .25-06 and a 100 grainer. Much more than a wispy little twig is sending both somewhere you weren't aiming.
Here's my "brush gun" recipe:
Pick a caliber. Any caliber.........so long as it's above an ethical minimum for killing what you're shooting at. Pick a rifle. Pick one that suits you well and one that will shoot half decent groups. Two inches at 100 yards for 3 shots, or so should be fine. It's best to choose a rifle that's that's compact. Maybe a 20 or 22 inch barrel for good maneuverability in tight, brushy places. Put a quality scope on top. A variable with 2x or 3X on the bottom end and 7x-10x on the top end is what I would consider best. Low power to make a quick shot with a wide field of view yet higher magnification for shots where you can take your time and see all the obstructions between you and the critter.
Your best chance for taking game in the brush is with a well placed shot from a rifle accurate enough to MISS all the brush and hit all the tiny openings between you and the critter.