It is named in Japan after the fabled figure Jack-O'-Lantern. According to the earliest accounts of the tale, "Stingy Jack" was an Irish farmer who persuaded the Devil not to take him to hell. When he was refused entry into heaven, he wandered the earth as a turnip-headed (or pumpkin-headed) soul who would come to be called "Jack of the Lantern" - or so says the legend. Jack-o'-lanterns are carved by children and enthusiasts alike on Halloween, though the tradition of carving gourds dates back probably to the dawn of mankind, and is not endemic to any particular culture. The tradition can also be thought to help guide the lost soul himself.
The legend, however, goes back further than the term itself. Jack-o'-lantern or some variation thereof was at the height of usage in 17th century Europe. Simply put, it meant "the guy with the lantern". Later the term would almost exclusively be used as slang in reference to the will-o'-the-wisp phenomenon, or ignis fatuus - due to the appearance of a far off person carrying a lantern.
Pyro Jack is second of the three Jack brothers. He is one of the most common demons in the series, appearing in nearly every game. He still retained the more traditional "Jack O'Lantern" name in the earlier English localizations. Since Shin Megami Tensei III: Nocturne and subsequent localizations, "Pyro Jack" has occupied the English naming with no official explanation from Atlus. The name change, however, makes him more comparable with his in-game brother, Jack Frost, in terms of their signature elements of fire and ice.
Shin Megami Tensei IMAGINE
"Imps of fire that appear in English legends. Jack-o'-Lantern is a soul who lived a decadent life and was refused entry into the afterlife. Taking pity on him, a demon placed a small bit of hellfire in a lantern made from a turnip to provide light for him as he wanders through the darkness. In the world of the living, he sometimes serves as a guide for travelers. Jack-o'-Lantern is good friends with Jack Frost. Some Demon Busters claim to have seen them team up as Demon Buster-busting duo Lantern Frost. Today, Jack-o'-Lantern is known as the pumpkin ghost of Halloween. It is believed that this change from turnip to pumpkin came about when the custom of Halloween first came to the United States, because Americans found that pumpkins were brighter and easier to carve than turnips."
—Shin Megami Tensei IMAGINE Compendium
Pyro Jack appears in Nakano field during the in-game night hours and a larger field boss variant spawns close to the New Moon moonphase. He frequently acts as the quest-giving NPC for Halloween and autumn-themed events. In particular, he was a supporting boss in the All in the Hopeless Afternoon Halloween event as Netherworld-Guiding Flame Pyro Jack that fought alongside Wandering Innocent Soul Alice.
He occasionally makes appearances supporting Jack Frost in Christmas-themed events enough to have his own special Christmas-themed variation. Like Jack Frost, he is one of the common bazaar-tending demons and many pieces of player gear are themed after his design. When equipping a weapon infused with his crystal, players can also gain the ability to use the Magic Shot skill.
Shin Megami Tensei: Strange Journey
"An Irish spirit, seen as flames in the swamp. Also known as the Jack-o'-Lantern. He is known around the world by names such as Will o'the Wisp and Hitodama. He appears at night to startle travelers and make them lose their way."
—Shin Megami Tensei: Strange Journey Compendium
Devil Summoner: Soul Hackers
"An Irish spirit, seen as a floating flame in the swamp. Also known as the Jack O'Lantern. He is known around the world by names such as Will-o'-the-Wisp and Hitodama, and is said to be the wandering spirits of the dead. He comes at night to startle travelers and make them lose their way."
—Soul Hackers 3DS Compendium
If Pyro Jack's loyalty is maxed out, he can be converted via Mystic Change into a set of Pumpkin Bombs, powerfully explosive shotgun shells.
Devil Summoner: Raidou Kuzunoha vs. The Soulless Army
"An Irish spirit, seen as flames in the swamp. Also known as Jack-o`-Lantern. Said to be the spirit of a man cursed to wander the earth with a lantern to see in the dark."
—Devil Summoner Devil Chart
Megami Ibunroku Persona
Pyro Jack as a Persona is the third Persona of the Lovers Arcana and as it ranks up its stat gains are relatively balanced. Upon being returned to the Velvet Room at MAX Rank, it will yield the Iron Pumpkin piece of equipment.
Pyro Jack, as a demon, begins appearing on the upper floors of the SEBEC Building in the company of a Jack Frost.
Persona 2: Innocent Sin
Excluding unique Persona, Pyro Jack is the fourth Persona of the Lovers Arcana. When the party encounters the demon Pyro Jack with him equipped as a Persona, they will initiate a conversation with each other which results in the demon Pyro Jack offering Lovers Tarot cards to ask the player to turn him into a Persona too.
Persona 3
"Also known as Jack O`Lantern, he was an Irish farmer who persuaded Satan not to take him to hell. When he was refused entry to heaven, he wandered earth as a pumpkin-headed soul."
—'Persona 3 FES Compendium
The fifth Persona of the Magician Arcana, Pyro Jack can be summoned by fusion, or through the Shuffle Time mechanic in the second block of Tartarus, Arqa.
Persona 4 The Animation
Pyro Jack, in Persona 4 The Animation, represents the bond between Yu and Yosuke. He was the first Persona that Yu summoned due to his newly obtained Wild Card ability. Early on, his abilities have assisted Yu in taking down both Shadow Chie and Shadow Yukiko with his Agi-based spells and Absorb Fire ability, and was used briefly during the Shadow Mitsuo battle.
Persona 4 Arena
While not making an in game appearance, one of Kintoki-Douji's alternative palettes resembles Pyro Jack.
Jack Bros.
Pyro Jack is one of the three initial playable characters in this spin-off title named after him and his brothers, Jack Frost and Jack Ripper, where he must return to the fairy world before midnight on Halloween. Unlike Frost and Ripper, he does not have an area he excels in, but is well-rounded stat-wise. In his character-specific ending, he realizes the Pixie that accompanied him through the labyrinth may be his world's princess.
DemiKids Light & Dark
"Flame-demon with a pumpkin head. Lures enemies into a bottomless swamp."
Known as Punkin, he can perform the combo Fire Flare with Sizzard and Redwing. Punkin also has the power Cliffhanger.
Digital Devil Saga: Avatar Tuner
Pyro Jack appears in Digital Devil Saga: Avatar Tuner as one of the "Hip Hop Brothers", who were members of the Solids. They attack Embryon at Coordinate 136 on the second floor. The other brother was Jack Frost. Pyro Jack shouts "Listen to me!" before casting his spells, possibly an allusion to the legend's persuasion of the devil.
Later in the game, the remaining HipHop Brother can be found guarding a large blue treasure chest in the entryway of Coordinate 136. After first denying the party access to the chest, he does enlist their help in retrieving the key to open it. After defeating Titania on the 3F - Transit floor, returning to Pyro Jack with the key will cause him to pop open the chest and run off with its contents in order to curry favor with King Frost. After defeating King Frost in the top room of the tower, Pyro Jack can be found cowering out on the balcony. Promising to follow Serph and begging for forgiveness.
Digital Devil Saga: Avatar Tuner 2
Pyro Jack appears in the Underground City later in the game and will sell Impel Stones he produces from his head for $50,000 a piece. These stones have the same effect as Psycho Rage and will grant 4 flashing press turns when used. Pyro Jack will not have another stone to sell until the one currently in the party's inventory is used.
During the last stages of the game, Pyro Jack's Solar Data can be found in the 2nd Layer of the Sun and will resume selling Impel Stones there.