Long winded video about it:

'Are solid objects really “solid”?' (go-to 7:30)

• https://www.youtube.com/watch?v=DqhXsEgLMJ0
• https://inv.nadeko.net/watch?v=DqhXsEgLMJ0

There's a bunch of these thought experiments that try to posit scenarios where C is violated.

Here's one I remember from uni involving scissors. Similar to what OP was thinking, but really really big scissors.

At this scale, the stick isn't as solid as your intuition would lead you to believe. Instead, you have to start thinking about the force at the atomic scale. The atoms in your hand have an outer shell of electrons which you use to impart a force to the electrons in the outer atoms of the stick on your end. That force needs to be transferred atom to atom inside the stick, much like a Newton's Cradle. Importantly, this transfer is not instantaneous, each "bump" takes time to propagate down the stick and will do so slower than the speed of light in a vacuum. It's basically a shockwave traveling down the length of the stick. The end result is that the light will get to the person on the other end before the sequence of sub-atomic bumps has the chance to get there.

This doesn't account for blinking.

If your friend blinks, they won't see the light, and thus would be unable to verify whether the method works or not.

But how does he know when to open his eyes? He can't keep them open forever. Say you flash the light once, and that's his signal to keep his eyes open. Okay, but how long do you wait before starting the experiment? If you do it immediately, he may not have enough time to react. If you wait too long, his eyes will dry out and he'll blink.

This is just not going to work. There are too many dependent variables.

How heavy would a stick of this size weigh?

why wouldn't this work

because bullets are faster than whatever the fuck speed stickman is achieving
and even bullets are slower than light

If you're openminded enough to listen to those who disagree with the standard model,
take an elastic band and turn one end. Instead of the band turning, you'll have a twist in your band
and it takes time to unravel the twist if you let go on the other end.
That's what will happen to the stick and this travels at lightspeed,
because this is how light works. Light works like 'the stick' in your example.
And if you try turning it faster the 'elastic band'/stick/'atom on the other end' starts breaking.

If you need FTL communication, then use gravity..somehow.

The pole would basically be a space elevator. I suspect gravity and inertia would effectively keep you from moving the stick. Even if you could move it, you'd only be able to move it at a speed that would seem like it's stationary. As such, the light would still be faster.

That's what he meant by we'll use sticks on the other side

Perfectly rigid sticks don't exist.

This wouldn't work because the moon is more than 300k km away :P

You're gonna want a powerful laser probably and ain't no stick that big like not even fkn close not even if we tried so that's why would'nt tbqh