Camae arrives with coffee and stays for what’s made to feel like a requisite examination of King’s demons. He’s on the road, elated and exhausted after a rousing church oration that day and, clearly, tantalized by the lively woman in his midst. In these introductory sequences, “The Mountaintop” holds out the promise of illuminating King in repose, of imagining what he might have been like in a state of unwinding, rather than as he’s more commonly depicted on the stump, wound up.

We find him in Room 306 desperate not for a cause, but for a smoke, and presciently anxious about the number of whites who seem to hate him. He reads aloud from a newspaper article about a bomb threat that had been called in about his plane from Atlanta. To which the feisty Camae replies: “Civil rights will kill you before them Pall Malls will.”

We should feel an intimacy developing between the maid and the legend. It never happens. What evolves is far less immersive. Part of the problem is casting: the 62-year-old Jackson, alas, is wrong for the 39-year-old King; the portrait is sort of passive, drained of life force: could King have turned the switch off on his own electricity so effectively? (Thirty-five years ago, Billy Dee Williams played King on Broadway in “I Have a Dream,” a short-lived show based on King’s writing.) It’s a matter of concern that the more dynamic character is Camae, who’s even given the evening’s most invigorating sermon, delivered astride a peach bedspread on David Gallo’s suitably realistic set.)

Still, Jackson’s less than perfect casting is not the fatal wound to this two-character piece, which won the dramatist London’s 2010 Olivier award for best play over “Jerusalem,” “Enron” and “Red.” (Hall is also one of the inaugural resident playwrights at Arena Stage, where she’s developing a play that will be presented in a forthcoming season.) What undermines “The Mountaintop” is a rather amateurish narrative twist that is apparently so pivotal to the evening’s reason-for-being that the show’s producers have asked reviewers not to reveal it.

There can be no ethical offense in reporting that this contrivance is what terminally weakened my faith in the play or that most of the audience will not find the revelation especially surprising, either. Constrained from going into detail, I can only say that once the device is introduced, the relationship between the characters ceases to be of much interest. Those who don’t react as strongly may find more in “The Mountaintop” to savor.