×Get the serpent to go down the passage in column 23 ahead of you, so the eye on the west has no brain path and gets stuck on the force arrow.

×The problem: You need to make a brained snake not follow you, which means having it make an unbrained move. What ways do we know about that let us achieve that?

×catching up to the serpent in time while not creating more than one tar baby on any cuts.

×Why are you cutting the tar after the serpent makes his way into the corridor?

×
I can't have tar at both spots indicated in this picture because then there's no orthogonal route into the corridor at all, so the serpent can't get in.

But if that's the case then, as far as I can tell, the serpent and I have to be on opposite sides of the tar.

...oh, wait. While typing that out, I realized what to do.

×The serpent has the wrong parity for it.

×You are correct that tar cannot be at both spots at the time the serpent wants to move into the corridor. It can be at one of the spots though.