Robert Allen, Pocket Fowler's Modern English Usage, second edition (2008) has this entry for "amok, amuck":
amok, amuck. The word is normally used in the phrase to run amok/amuck, meaning 'to run about wildly in a violent rage', and is an extension of a particular meaning in Malay anthropology (Edward now wore the manic look of some animal transferred into the wrong environment. as though he might run amok, or bite — Penelope Lively 1990). It also has figurative uses not involving physical action (With Thatcher running amok through the welfare state, lobby groups are preoccupied defending what was once thought unassailable — New Scientist, 1991 | It wasn't his fault that her feelings seemed to be running amok — E. Rees, 1992). Occasional unidiomatic uses occur (The place was amok with running kids with running noses — weblog, BrE 2005 {OEC}). The spelling amok, which is closer to the original Malay amoq meaning attaching in frenzy', is more common (five times more in the OEC) and is preferable.
Interestingly, neither Henry Fowler, A Dictionary of Modern English (1926) nor Fowler & Ernest Gower, A Dictionary of Modern English, second edition (1965) pay any attention to what verbs go with the word. Instead both focus on criticizing use of the spelling amok (as opposed to amuck) as a snooty affectation:
amuck, the familiar spelling, due to popular etymology, but going back to the seventeenth century & well established, should be maintained against the DIDACTICISM amok.
In any event, although it is somewhat unusual to come across other verbs than run (and go) paired with amok in published writings, it isn't terribly difficult to find them on purpose. Here are some verb + amok pairings that Google Books searches turn up.
From "Breeders' Queries," in Eggs and the Intensive World (February 23, 1916):
If, however, you use a White Leghorn cock on Ancona hens, the two breeds are so much alike in respect to the various essentials to fecundity that one cannot prove entirely dominant over the other; they both struggle for dominancy and the result is that both come "amok" with the result that the progeny which represents neither parent in particular, so far as fecundity is concerned , favours a reversionary type, and it is, therefore quite moderate in respect to laying.
From Arthur Whitten Brown & Alan Bott, Flying the Atlantic in Sixteen Hours: With a Discussion of Aircraft in Commerce and Transportation (1920):
This [extreme loss of vision after entering a thick bank of cloud] was entirely unexpected; and, separated suddenly from external guidance, we lost our instinct of balance. The machine, left to its own devices, swung, flew amok, and began to perform circus tricks.
From Kenneth Williamson & John Morton Boyd, A Mosaic of Islands (1963) [snippet view]:
A likely explanation was that some over-excited youth had struck before the captain had selected his prey, and perhaps the cheering of the crowd had alarmed the uneasy beasts at the critical moment when the wounded [whale] calf swam amok in pain and fear, stampeding the rest of the school away from the shore.
From Mary Luke, Catherine, the Queen (1967) [combined snippets]:
Soon these Highlanders, to the amazement of the English, had thrown away their shields, their broadswords and axes, and in a half-naked frenzy rushed amok into the teeth of the battle. The English closed ranks, readied their cannon, aimed their bows and slaughtered the infuriated Scots as they advanced.
From Mad and Magnificent Yankees: A New England Portrait Gallery (1973) [combined snippets]:
The possibilities apparent during speculations on "chance" would, I take pleasure in believing drive amok the most sophisticated of computers. But the majority of the lives about which you'll soon be reading were (or are) successful or disastrous due to both chance and taking a chance, which, in essence, is what "deviating from regularity" is all about.
From Marshall Frady, Southerners, a Journalist's Odyssey (1980) [combined snippets]:
It was a rather startling processional—suggesting some unlikely yawping many-limbed beast suddenly loose and charging amok through the corridors of the capital—and as it brawled on up the marble staircase to the main floor, one had a sense of being in the middle of some Latin American midnight coup: there was about it a definite if totally gratuitous air of some attack, rush, strike, with a furious urgency of its own, completely detached from the absolute absence of suspense in the procedure in the house chamber which had birthed and released it.
From Robert Pohle, Douglas Hart & Christopher Lee, The Films of Christopher Lee (1983):
One of the last episodes, with Diana Rigg as Mrs. Emma Peel, featured Lee as a man named Stone who is continually run over by the same motorist only to return to "life" time after time. Stone also seems to be sent amok by certain electrical frequencies, which cause him to behave in a markedly Frankensteinian manner--and, indeed, he turns out to be a robot double of the "real" Stone.
From an unidentified article in Oral Tradition, volume 8 (1993) [snippet view]:
Except as parody—not only of Akhilleus descending amok on hapless Trojans, but possibly even also of Odysseus' escape by ship from the clutches of the Kyklops—this characterization is at first sight hard to reconcile with the image of the honeyed, fluent speaker of Iliad.
From Elana Sisto, Fairy Tales: Portrait Paintings by Elena Sisto (1999) [combined snippets]:
Now, the giant galloped amok upon the lands, dear friends, as, in his madness, he tore stands of oak and birch and flung them this way and that, and a blindness fell upon him like a fever, and a terrible ringing like of a thousand bells did assail his ears, and he knew himself to have come to a fork in the road in the deserted netherlands beyond all our maps.
From W. T. Lhamon, Raising Cain: Blackface Performance from Jim Crow to Hip Hop (1998):
How is it people do not rampage amok? Postwar social theory increasingly answers such musings by arguing that crowds are composed of isolated, atomized persons. Each atom is violated by externally imposed principles that support control rather than individual or small-group agency.
From Maury Dean, Rock N Roll Gold Rush: A Singles Un-Cyclopedia (2003):
No angel, Willie [Nelson] partied amok with his hi-jinx entourage, yearning to get back “On the Road Again” (#20, 9-80, and #1 C, as a follow-up to Bob Wills's masterpiece “Faded Love” at #3 C for Willie in earlier 8-80).
From Arthur Saltzman, Nearer: Essays (2006):
He progressed by hunching forward as if his body were a machine he had to learn to operate like someone else's car—the gears were positioned differently, or they slipped at unexpected stages; the shifts felt funny, anfd it would take time to accustom himself to the diminished dash. Is it possible to walk amok? He was walking amok.
Leaving the hospital, I felt like those students who know they've blown the midterm. “He never said this would be on the test!” they complain as they slink away, amok. Lowing the last-ditch lament of the done-for.
From Dennis Barrer Jr., Templars and Pagans (2010):
Then the Templar paladin entered into the rear of the stable via the back door undetected and crouched down to observe the noisy activity of Norman soldiers scampering amok all over the place through one of the open stable doors exiting into the sandstone courtyard from afar while hearing the meager sounds of men's voices and footsteps being created by these unwelcome trespassers vibrating through his argent steel helmet that had entered his eardrums.
From Jonathan Robinson, On It (2014):
Back to work I went – and started slashing amok like a rampaging knight in armour. Following Joanna Trollope's sound advice, friends – the few I had left – who had been made to endure the first draft were redeployed to read early stages of the cut version.
From Anna Erishkigal, The Caliphate: A Post-Apocalyptic Suspense Novel (2016):
Rasullullah gives me a cruel grin as he slides my glove down to expose my entire wrist. A crowd begins to gather. Men. Curious about whatever woman fell amok of the al-Khansaa's purity rules.
I think that the word Erishkigal is looking for here is afoul, not amok—but it's her book.
From a 2021 translation by Shadi Bartsch of Vergil's Aeneid (published by Modern Library):
Now they shouted louder, maddened by / the omen. Some snatched fire from nearby hearths, / others robbed the altars. They hurled branches, leaves, / and burning torches at the ships. Fire raged / amok over the seats and oars and painted sterns.
From Isaac Nasri, Into the Violet Gardens (2021):
The odds prevail. The Gorillax pilot fires one of his cannons, hitting the hacker squarely in mid-air, and curtis's limbs splatter. Horrified, the officers scatter amok, leaving the pilot to glares at the one vulnerable human behind the v-front lens as it raises its gargantuan hands.
Obviously, some of these instances involve more apt uses of amok than others—and some (like the 1916 instance of "come 'amok'") are simply perplexing.