In a way, it's fitting that there's a whole chapter named "Mr. Jerome is Afraid," because that's the overwhelming sense that we get from Mr. Jerome: fear. He's a squirrely little man who is obviously very afraid of the woman in black that Arthur is seeing, but won't tell him anything about her. He won't even explain why he's so terrified of going to Eel Marsh House, just repeating again and again that he can't help Arthur:
He shifted his chair back, further away from me, as he sat behind his rickety desk, so that I thought that, if he could have gone through the wall into the street, he would like to have done so.
"I'm afraid I can't offer you help, Mr. Kipps. Oh, no." (7.21-22)
When Arthur keeps pressing further about the woman in black, Jerome just gives the most annoyingly vague answer ever.
When he spoke again he sounded husky and tired. "There are stories," he said, "tales. There's all that nonsense." (7.36)
Jerome seems represents the prevailing attitudes of the town, which involve being fearful but extremely vague when pressed for answers. They've got a bit of a She-Who-Must-Not-Be-Named situation going on with the woman in black—they're so scared of her that they won't even talk about the things she's done.
Or allegedly done. Notice how he calls the situations "tales" and "nonsense," but he still won't take over the job? Yeah, we're pretty sure this guy believes in ghosts.