How does the narrator feel after leaving the signalman following his second visit?

When the narrator leaves the signal man's hut for the second time, he is extremely concerned, for several reasons. First of all, he is pained on behalf of the signal man as a person: he is evidently struggling with his conscience, and possibly with, the narrator seems to indicate, some kind of mental strain, and the narrator doesn't want him to suffer in this way. Secondly, he is also concerned for "public safety" as a result of his concern for the man's state of mind—in his position, he is responsible for the safety of everyone on and near the railway line, and should something happen to him, terrible consequences could arise. The narrator feels burdened by the knowledge of what a state the signal man is in, and is tortured as to what he should do. He feels partially as if he should tell the man's superiors what he knows, but ultimately decides that this would be treachery on his part. Instead, he decides to take a "middle" ground and accompany the man to a doctor.

After his second visit, the narrator feels very concerned for the emotional and psychological well-being of the signalman. Note, for example, that the narrator offers to spend the night in the signal box but that the signalman will not hear of it. This shows that the narrator feels a genuine sense of compassion toward the signalman.
Moreover,  after their conversations, the narrator knows that the signalman is an "intelligent" and  "vigilant" person. However, given the events that have happened, the narrator wonders how long the signalman will remain this way.
It is clear, then, that the narrator believes the signalman's story and is worried about the signalman's state of mind. You will notice that the narrator looks back at the red light more than once as he leaves the signal box, a sign that he understands and shares the signalman's fears and concerns. 
The narrator plans to return to the signalman the next day and accompany him to a medical doctor to prove his version of events. This desire to help the signalman further reinforces the narrator's genuine sense of concern toward the signalman.