Although it is true that O. Henry does not explicitly say what John Perkins' characteristics are, you can infer them from how he behaves in the story.

The first thing you can see is that John is very much a creature of habit.  He does the same thing over and over just because he is used to doing it.  (This is one reason why the story is called "The Pendulum -- something that keeps doing the same thing.)

John walked slowly toward his flat. Slowly, because in the lexicon
of his daily life there was no such word as "perhaps." There are no
surprises awaiting a man who has been married two years and lives in
a flat. As he walked John Perkins prophesied to himself with gloomy
and downtrodden cynicism the foregone conclusions of the monotonous
day.

We also know he doesn't look inside himself very much.  We are told that he doesn't think about his emotions much.

So, overall, he is something like a machine -- he just does the same thing over and over without really thinking much about it.

In the story, he tries to break out, but when his wife comes back they go back to the same old routine.

Nobody heard the click and rattle of the cog-wheels as the third-floor
front of the Frogmore flats buzzed its machinery back into the Order
of Things. A band slipped, a spring was touched, the gear was adjusted
and the wheels revolve in their old orbit.