There’s a lot going on in “American Made,” a hectic, hyperactive true-life tall tale that jumbles Colombian drug-smuggling, CIA arms-trading, Midwestern fortune-making and a whole lot of very fancy flying. Yet the most salient image in the whole coked-up kaleidoscope is a simple one: Tom Cruise’s sunglasses. There may be significant stretches in Doug Liman’s film where the star, as TWA pilot turned all-sides-of-the-law hustler Barry Seal, isn’t wearing wire-rimmed aviator shades, yet somehow it feels as if they’re always there. An accessory that Cruise made wholly his own in “Top Gun,” they connote as much rakish bravado and slightly impenetrable machismo now as they did then — 1986, coincidentally the year that the action in “American Made,” which spans eight fast years of Carter-to-Reagan-era governmental skulduggery, comes to a startling head.

A sweat-slicked, exhausting but glibly entertaining escapade on its own terms, “American Made” is more interesting as a showcase for the dateless elasticity of Cruise’s star power. It feels, for better or worse, like a film he could have made at almost any point in the last 30 years: As Cruise’s character here puts his prodigious aviation skills to wildly irresponsible use, it’s tempting to imagine Liman’s film as an oblique spiritual follow-up to the adventures of flashy Navy pilot Pete “Maverick” Mitchell, beating tardy forthcoming sequel “Top Gun: Maverick” to the punch. The films’ worlds might be very different, not least since “American Made” counts as fast-and-loose non-fiction, but Cruise’s presence across them, all Colgate grin and cock-of-the-walk swagger, is notably consistent. (Even period authenticity has no dominion over him: While his co-stars are slathered in late-1970s and ’80s kitsch, Cruise’s hair and costuming throughout can scarcely be linked to any milieu.)

It’s frankly a relief to see Cruise acting this assertively himself again (give or take a mild Louisiana drawl) after watching his leading-man persona anonymously shoehorned into the established franchise constraints of “The Mummy” earlier this summer. What the actual Barry Seal may have been like is almost impossible to glean from his performance; this is a star vehicle first and foremost, which makes the film’s balancing of fact and fancy even harder to parse. Gary Spinelli’s script follows in the recent tradition of “War Dogs,” “Gold” and “American Hustle” — all high-flown, fact-based tangles of individual and institutional corruption — by blatantly owning up to the absurdity of its real-life premise. “Shit gets really crazy from here,” Seal even admits in one of several grainy, after-the-fact camcorder confessionals, a somewhat clunky framing device the film uses in lieu of voiceover.

Things are already pretty chaotic to begin with, as the film opens with a standard-issue disco-era swirl of archive footage (including, cutely, a vintage Universal Pictures logo at the outset) and jaunty airborne antics. All set to Walter Murphy’s “A Fifth of Beethoven” — kicking off a peppy jukebox soundtrack that later reaches its on-the-nose thematic apotheosis with Talking Heads’ “Slippery People” — this intro swiftly establishes Seal as a devil-may-care playboy in TWA uniform. The year is 1978 and Seal is bored of his domestic flight path, keeping himself amused with the odd bit of cigar smuggling and faked inflight turbulence. When he’s approached by CIA man Schafer (Domhnall Gleeson, laying on the alpha smarm) to fly undercover for them instead, skimming Central America to take surveillance photos, he’s only too quick to accept.

If Seal’s wife Lucy (Sarah Wright Olsen) and two children back in Baton Rouge are secondary considerations to him, the film treats them likewise: Doing her best with scant material from the script and wardrobe department alike, Wright Olsen is mostly limited to fretful chiding on the sidelines as her husband’s covert career veers off course. Which it does, in rapidly escalating but dizzyingly lucrative fashion: An illicit sideline in transporting cocaine from Colombia for the Medellín Cartel is soon co-opted by the CIA into a major gun-running racket, while Seal’s new home base in back-of-beyond Arkansas becomes a military training ground for the Contras.

To go by the film’s account, Seal simply winked and smiled his way into becoming a critical player in the Iran-Contra affair of the mid-1980s, and his blithe detachment from the political specifics of the scandal (he admits to an affection for Ronald Reagan, but principally on the basis of “Bedtime for Bonzo”) brings to mind a smoother-operating Forrest Gump. As major figures like Pablo Escobar and Manuel Noriega flit through the film in incidental cameos, Seal remains the mostly charmed, accidental center of it all.

Fusing the lickety-split comedy of his “Swingers” days with the more businesslike action smarts of his latter-day Hollywood works, Liman does his best to keep this top-heavy narrative in constant motion — without approaching the technical or structural inventiveness of his previous Cruise collaboration, 2014’s undervalued sci-fi mindbender “Edge of Tomorrow.” Enlisting “City of God” cinematographer César Charlone proves a canny move, as the Uruguayan’s roving, agitated camera style (not to mention a perspiring, overripe palette, heavy on hot yellows) implies antsy tension even in comparatively banal domestic scenes.

As storytelling, however, “American Made” is both so distracted and so distracting that there’s barely time to consider what it all adds up to. Beneath Cruise’s unruffled commandeering lies a messy array of secondary characters somewhat haphazardly chopped into proceedings by editor Andrew Mondshein. (Dylan Tichenor and Saar Klein are credited with additional cutting.) From Seal’s redneck brother-in-law (a typically slithering Caleb Landry Jones) to a suspicious local sheriff (Jesse Plemons, who seems to have suffered most in the edit), such figures add little color or credibility to the film’s comic-book reportage.

In the film’s press materials, Spinelli admits to being in thrall to Martin Scorsese’s “GoodFellas,” and the influence is particularly clear in a headlong final act that deals with the souring of Seal’s questionably achieved American dream. But “American Made” lacks the sense of moral reckoning and self-effacing human irony it needs to achieve the emotional payoff or tragicomic heft of “American Hustle,” let alone Scorsese’s masterwork. Based on a true story or otherwise, it winds up simply as another sharp, spit-shined Tom Cruise jet, and not a bad one at that: The genius of Cruise’s superstardom may be that he can make even the scuzziest American scoundrel seem, like Ethan Hunt or Maverick Mitchell, untouchably heroic. When those aviators are on, all bets are off.