The cuckoo clock analogy doesn't work as its entirely physically causal. The ticking is a physical resistance to moving cogs and springs, and can be measured physically.
And how do you support the idea that the brain is not?
I mean, imagine that a tribe of primitive amazonian aborigines were to be given a cuckoo clock and told how to wind it. They don't know the physics behind it, nor understand how those cogs make it keep time. Don't you think they MIGHT come up with some dualist scheme where there's some non-material The Timekeeping entity that's separated from the physical cogs?
In fact, you don't even have to imagine a tribe, you can look at real history. The ancients imagined such dualist schemes to explain why the universe does the things it does. E.g., the divine Logos, translated as "Word" in the KJV, but more properly meaning "reason" was just that. The "mind" of the universe, if you will. That which makes the planets move, and at that in always those orbits. That which makes the Sun rise every morning. That which makes it be cold in winter and warm in summer.
Nowadays we know that it's just physics. There is no Logos moving the matter in the movement of the planets, there is only matter interacting with other matter. (Ok, distorting the space, but let's keep it simple.) There is no Logos making it cold in winter and warm in summer, it's only a matter of how many photons you get per square foot. Etc.
That's not even the only one. Dualistic schemes and sometimes whole layered schemes of non-material entities were once the name of the game. Everyone had one or a few to explain why the world works. But invariably we discovered that they're wrong. There is no logos, there are no Aeons and Archons governing the principles of physics, there is no mind and free will of the atoms, and generally there never is the second half of those dualism schemes. It's always just matter and energy interacting with other matter and energy, in very mundane and predictable ways.
What makes you think YOUR dualism scheme is any better, especially in the face of evidence to the contrary.
But let's return to our hypothetical tribesmen and imagine them applying a more scientific approach. They can't tell why those cogs make the clock keeps time, but they CAN see that if you hold onto one of the weights to stop or slow down the cogs, then the timekeeping stops or goes all wrong too. They could see that if you take a cog out, the timekeeping goes downhill. They can see that if you swap the clock arms around, the clock starts showing the wrong time. They can see that if you move the arms to the wrong time, it will keep showing the wrong time. Etc.
Basically, if they were smart and skeptical, should they not conclude that there is nothing magical or transcending materialism in that Timekeeping? Should they not conclude that there is no separate The Timekeeping entity there, but just cogs moving other cogs, i.e., matter moving matter? Should they not conclude that that Timekeeping is just a name for what those cogs DO?
Well, we're largely at the same point with the brain. We know that neurons excite other neurons. We know what substances act in which synapses. We know what substances or lack thereof make someone's mind do funny stuff. And they shouldn't if the mind was a different entity and wasn't actually a function of those neurons. We can on MRI see which lobes fire up when the mind does this or that. We know what damage to those lobes does to the mind. Etc.
Should we not conclude, just like with cogs and timekeeping, that "The Mind" is nothing more than a name for what those neurons do for a living?