You can't "condition" the head, regardless of what some people may claim. As an athletic trainer (sports medicine, not personal trainer), I've easily learned that head trauma leads to more head trauma requiring less force.
There's no ethical scientific way to prove this though. To do so, you'd need to intentionally hit people in the head and measure the force required over and over again.
In the 15 or so years I spent as an ATC (most of them being NCAA Div I with collision sports such as football and hockey, and men's soccer), most often athletes who had a concussion had more than one in their career. I found the highest rates of concussions were ice hockey and soccer. Ice hockey was due to a combination of the speed of skating, the hard surfaces of the ice and boards, and the helmets were inadequate.
Soccer has the most relevance in this discussion IMO. That was most likely attributed to the repetitive heading of the ball. In highly skilled athletes, the ball itself caused very few concussions, but it took less force to cause a concussion from hitting heads, being elbowed, or hitting the ground.
All my findings are anecdotal, not empirical. There's no ethical scientific way of solidly proving nor disproving this. But seeing the same things over and over again becomes painfully obvious (no pun intended).
The best way to avoid brain damage in boxing (or any other collision or contact sport) is to avoid getting hit. Boxing teaches movement, defensive and offensive to avoid being hit. Not just keeping your hands up and moving away from what you see coming, but to move and not move certain directions before, during, and after an exchange.
Tommy Morrison had a great quote after he was KOed by a nobody - "Give any fighter who's over 200 lbs a clean shot at your head, and they're going to knock you out cold." He was criticized as having a "glass jaw." It wasn't his jaw, it was his lack of defense, more specifically his poor movement away from punches and his hands being down at key moments.
Anyone who actually knows how to throw a punch will KO you with a clean shot at your head every time.
As others have said, learn to move, and spar with people who'll hit you light enough to remind and point out your mistakes.
Without any solid scientific proof (again), the most effective way to reduce head trauma (including not being hit in the first place) is neck strengthening, theoretically speaking. The neck will act as a break, slowing down your head from a whiplash-like effect, reducing the frequency and severity of your brain bouncing back and forth inside your skull.
