Kenneth Branagh, so busy directing blockbuster films including “Thor” and launching his own London-based theater company, has been negligent in his duties as an actor.

“Wallander,” a member of “Masterpiece Mystery!” since 2008, is a notable exception — and a rather peculiar one for a performer who can rattle off Shakespeare soliloquies the way mere mortals recite the alphabet and whose portrayal of a defiant Franklin D. Roosevelt in 2005’s “Warm Springs” remains one of TV’s most energetic, crackling performances.

Kurt Wallander has nothing in common with FDR. The Swedish inspector has an almost allergic reaction to speaking. Every part of his body seems to wince if a stranger dares to touch him on the shoulder. No thanks on the whiskey; bottled water will do just fine.

In this weekend’s episode, the first of what PBS is billing as the final three chapters in the series, our hero is so invisible to his drunken colleagues at a South Africa police conference that they’re oblivious to him when he walks past their two-fisted festivities, despite the fact that he’s being marched through the hotel lobby at gunpoint.

But even in this first installment, in which a routine missing-person case leads to signs of political corruption and a high-profile assassination, there are hints that a dramatic personal crisis is creeping into the life of our otherwise drab detective. Is the African sun to blame for blackouts and dizzy spells? Or is it something else?

That mystery deepens over the course of the following two weeks when Wallander returns to his home base of Ystad, a burg cursed with more perplexing murders than Jessica Fletcher’s Cabot Cove. While investigating the disappearance of a troubled girl and the apparent suicide of an in-law, the sleuth starts to slip, forgetting to turn off the gas on his stove, leaving his weapon in a pizzeria and even letting key suspects dash into the night while he spaces out.

Alzheimer’s disease has been the driving force of the series and Henning Mankell’s novels, both of which treat the whodunits as distractions from its primary mission: slowly peeling off the layers of its introverted title character. (The mysteries, as always, are as challenging as trying to decipher the instruction manual for that bookshelf you bought from Ikea.)

The personal examination, and the exploration of dementia in general, couldn’t ask for a better accomplice than Branagh. He handles his mind’s slow deterioration with the same subtleties he brings to scenes in which he attempts to fit in at a high-society cocktail party, preferring to mix with the paintings on the foyer walls.

Branagh doesn’t give himself permission to rage against the machine until the end of the trilogy, when dementia temporarily takes over, causing him to strip off his clothes in a field, ranting nonsense, unable to recognize his beloved daughter.

It appears to be a nod to King Lear, a character the 55-year-old actor is still too young to play, but it’s a tantalizing tease of what’s to come a decade from now — as long as he’s willing to tear himself from helming “Thor VII: Greased Lightning.”

For now, “Wallander” will have to do. Twitter: @nealjustin