An insensible hexagon

The puzzle is (almost) self-contained in the grid above. You can "move" from a tile of the grid to another if they share at least a vertex. After the maze is complete six things will clue to the solution which is an English phrase composed of four words of lenght 3,7, 7 and 10 letters.

EDIT: I’ve updated the picture due to an error (call it a typo). This edit does not impact the method that should be used to find the solution, the solution itself changes only a little bit.
Pleas don’t look at the edit history if you want to solve this puzzle from scratch, otherwise it will be too simple.