Whatever the “Diagnostic and Statistical Manual of Mental Disorders (DSM)” has to say on the subject, the movies have long maintained that there’s a thin line between “loveable eccentric” and “mentally ill.” While we’ve (mostly) progressed beyond the “all the mentally broken really need is love” cure in screenplays, the original trope and that always “thin line” is ever with us.

“The Electrical Life of Louis Wain” skips back and forth across that line. It’s a giddy then sad and somewhat forlorn biography of a great English illustrator and a man the film maintains was Britain’s original “cat fancier.”

Before Louis Wain, cats were “useful” as “mousers” and little else. But when Wain and his wife took one in as a pet, and he then started painting them, illustrating them in either cuddly and adorable poses, or silly settings (cats playing cards, golf), dog-mad Britannia went feline fur baby crazy.

And when he and his work came to America, we followed the Mother Country off that cliff.

Wain makes another grand eccentric in the repertoire of Benedict Cumberbatch. Working from a script by Simon Stephenson and the film’s director, Will Sharpe, Cumberbatch creates a somewhat manic polymath — or “poly-hobbyist,” as our droll narrator (Oscar winner Olivia Colman) describes him. Antic, full of “patents” and theories and ideas for art, he’s “on the spectrum,” we’d say today. The Victorians didn’t know what to make of him.

He pitches an opera to a famous composer without knowing how to write music, sees “electricity” everywhere, as the driving force of life and death, jumps into a bullring to get a better view of an animal he wants to draw and is scolded for his “imbecility” in big and small ways by the publisher (Toby Jones) of “The Illustrated London News.” That’s the publication that wants to hire him “at poverty wages” to be their pre-newspaper photographer illustrator of people, street scenes, fairs, sporting events, etc.

As he paints with both hands at once, Wain is unnaturally fast at this. He confesses he doesn’t “find this sort of work particularly taxing.” What convinces him to take the job are the fact that his widowed mother and his five unmarried sisters live under a home he’s supposed to provide them with.

And bossy, practical oldest sister Caroline (Andrea Riseborough, who makes a grand harridan) has hired a governess for the three youngest sisters. The governess, our narrator wryly informs us, makes Louis “tingly” inside. As he doesn’t “really know what the hell is going on,” he’ll take the job to employ the governess and try to sort out this “tingly” business in the company of Miss Emily Richardson.

She’s played by Claire Foy of “The Crown” and “The Girl in the Spider’s Web.” So we get the attrraction.

Actor-turned-co-writer/director Will Sharpe’s tale is told in three acts, with the first a sort of “Miss Potter/Personal History of David Copperfield” romance between two smart, quirky oddballs from “different stations in life.” The second is where fame, success and tragedy weigh in. And the third act tells us of Wain’s greatest fame and most debilitating tragedy.

Sharpe (“The Darkest Universe”) employs color-blind casting, peopling Victorian Britain and Edwardian America (look for a Taika Waititi newspaper editor cameo) with faces with India and Africa in their heritage as fellow train travelers, friends (Richard Ayoade), boxers and business associates.

Wain liked to pay prize fighters to let him get in the ring with them, with gloves not brushes. Add that to his early obsession with and wild theories about electricity, and his later certainty that taking cats in as pets would cause them to rapidly evolve into big blue-eyed, hind-legs walking companions who converse with their hosts, and you can see how the Victorians, Edwardians and others would have regarded this fellow as something of a nut.

Cumberbatch brings a twitchy, bird-like quality to Wain, who uses constant motion to keep his demons at bay because, our narrator tells us, “His mind was a dark, screaming hurricane of crippling anxiety and recurring nightmares.”

His childhood fears are related in old-fashioned, black-and-white “iris-in” flashbacks. His way of seeing the world pops up in scenery that morphs from photography to colorful illustration.

The leads have splendid chemistry, with Foye matching Cumberbatch in studied, intense oddness — antic line-readings, wide eyes darting at the sparks each recognizes that they’re setting off with the other.

And Jones is well-cast as the kindly, Dickensian employer who gives Wain a break, a light kick and a safety net, when need be.

The first act is so upbeat and charming that when things turn sour, it can feel like a sucker punch. But the “decline and fall” isn’t precipitous, the adoration by the now-cat-worshipping masses and the richly-detailed settings make our tumble to the ground, like Wain’s, slower. That softens the blows to come.

Although the later acts slacken the pace and earn this “Electrical Life” something of a downer vibe at times, I found it fascinating even when the thrilling first 45 minutes recede into the sunset.

This won’t be the eccentric character that wins Cumberbatch an Oscar. But fans of his, of lovely recreations of Victorian Britain (skimming past its “bizarre social prejudices”) and cat lovers will find much to embrace and enjoy here. Especially the cat lovers.

Rating: PG-13 for some thematic material and strong language.

Cast: Benedict Cumberbatch, Claire Foye, Andrea Riseborough, Toby Jones, Richard Ayoade, Dorothy Atkinson, Crystal Clarke, narrated by Olivia Colman

Credits: Directed by Will Sharpe, script by Simon Stephenson and Will Sharpe. An Amazon Studios release.’

Running time: 1:52