Merry Christmas and Happy Holidays. Consider this a little gift to you. It says you can keep it.
Kilroy is in many ways the Phantom stranger, the Keyser Sose of the Second World War. The question of what he/she/it was demands multiple answers.
She lost her family to the Nazis and arrived in the USA as a refugee. Her country of origin and any other details before the arrival were classified need to know. It was in a stateside hospital that her talent manifested. The Walking Darkness strode the wards frightening staff and patients alike, appearing and disappearing at will. Seldom glimpsed it was described as a shadow man with green glowing eyes. Several favors were called in mystics and mystery men were brought to investigate. The thing was finally caught in a sub-basement where it held off several costumed heroes until a wizard could trap it in a ward and trace it to its source: the nightmares of a badly abused girl.
With occult training the girl learned to project the creature, codenamed Killroy, at will. Killroy's handler fell into a trance when she projected Killroy. As a mental construct the thing could teleport at will. The maximum range of its ability was never found. The further the distance the quicker it had to return to its maker. Teleporting from England into Occupied France was doable with a duration of a couple of hours. It was theorized Killroy could teleport anywhere in the world for a few minutes at least. Most dsturbing was its ability to assume human form for a few minutes, usually that of a trusted person, once the Fuehrer himself.
Killroy was mute or at least never spoke to the Army handlers seeing to it and the creator. It knew how to read and write in German and English and would write down information it gathered or draw maps. The creature possessed almost total recall. It liked to sign its work.
The girl never had any recollection of this when she woke. Killroy seemed to be a separate personality and some thought she didn't create it so much as call it. Killroy never used weapons. It also possessed a wicked sense of humor leaving its victims in little tableaus, like the Ahnenerbe Major with the sword collection. Eventually it was used with the Special forces on a few missions. The rest of the team put up with it and its love of graffiti (you could bribe it with paint or markers.)
Killroys are creatures of the mind. Probably. They act out the impulses of their creator. Mostly. This usually means seeking the destruction of a particular person or group by any means. A Killroy is run as a character and seems to know what the creator knows. Briefings are with the human involved not the creature. The Army lost a few officers before they learned that trick.
Level XP HD BHB ST
1 2,500 2+1 +1 14
2 5,000 3 +2 13
3 7,500 4 +3 12
4 10,000 5 +4 11
5 15,000 6 +5 10
A Killroy moves 15. It can hide in shadows (Special Forces teams have a 1 in 10 chance of noticing one others a 1 in 20). The thing attacks with two claws doing 1d6 each. If a Killroy takes a person by surprise its attacks will be +2 to hit and do double damage. First level characters must make a saving throw or be frozen in place when they see a Killroy for the first time.
Killroys roll to increase Dexterity and Intelligence twice at each level. They attack with advantage from shadows and characters roll with disadvantage to detect them (if there's even any possibility. Ref's call.) A first level character can be frozen for a single round by a Killroy that makes a Charisma test will freeze a first level or 1HD opponent in place for a single turn the first time it is seen.