| This is material related to the Five Earths, All in a Row campaign setting |
While this is part of the Five Earths, All in a Row setting there are components in GURPS Fantasy and GURPS Thaumatology.
Humans (and, indeed, many other sapient species) have a tendency to become emotional invested in practically anything, and the things we are most invested in, we often tend to anthropomorphize (assign human traits to... or Martian traits, or Rigellian traits, et cetra, changing 'anthrop-' to the appropriate prefix). We even name specific types of personifications, such as genius loci, or tsukumogami, though how anthropomorphic they are varies.
Any item or location that at least one person is emotionally invested in for some time will eventually develop a thoughtform associated with it, even if the thoughtform only 'sleeps', rarely or never doing anything on its own (which is the case with most such thoughtforms, unless external efforts 'wake' them). The more people, the longer the time, and the greater the emotional investment(s), the more powerful that spirit (or those spirits) can become.
One sure way to 'wake' a spirit, if it's present at all, is to enchant the item it lives in. A normal enchantment binds an already awake thoughtform, sometimes generated by the caster during or leading up to the ceremony, to an item that itself lacks a spirit. If a spirit already inhabits the item, any of several things might happen: the thoughtforms might cohabit the item, they might merge (it is sometimes difficult to tell the difference between these first two; see below), they might come into conflict (with potentially nasty consequences for the caster and surroundings, depending on how powerful each is), or one might absorb the other; the latter is often the case when the caster is generating a new thoughtform, as the older spirit absorbs the power and patterns before the new thoughtform can properly take shape, sometimes even using its own energy to help the caster or casters work. Older spirits (and perhaps those 'born old' on Inp-Earth, after Goddard's Probe arrived, if they did not exist before) are often easier to enhance, as they have a better idea of how to help the caster or casters - and may be more enthusiastic about it, as well as more powerful to start with - (though this was not well known before the USAF, USN, and USMC made a policy to only or preferably transfer older aircraft to the USSF), unless the physical body the spirit is attached to is too big, as larger objects are harder to conceive as a whole piece. In that case, it is easier to enhance the separate parts, and let them come together in the vessel or location.
Spirits being spirits, they may simultaneously be separate intelligences, and components of the same intelligence, with varying degrees of sapience and sentience. The various enhanced parts of a car or ship, an aeroplane or spacecraft, are both separate magic items, and parts of the vehicle, just as their spirits may be separate spirits while still being part of the vessel's spirit. Likewise, the spirits of each college at Oxford are both individual entities, and components of the spirit of the University of Oxford, which is part of both the spirit of 'the British Universities' and the spirit of the city of Oxford. The spirit of the city is both an individual, and a vital part of the spirit of the ceremonial county of Oxfordshire, itself part of the spirit of England, which is part of the spirits of Great Britain, the British Isles, and the United Kingdom of Great Britain and Northern Ireland. The latter is still the heart of the spirit of the British Empire, even if on Inp-Earth, the latter exists mainly in the weaker name of the Commonwealth of Nations, which overlaps in large part with the spirit of the Anglosphere... again, while all still being individuals.
On the question of the Ship of Theseus, the vessel will tend to still be Theseus's ship (in the sense of having the spirit of Theseus's ship), even with all the original parts replaced: the spirit of a vehicle will tend to stay with the most intact form of that vehicle, even if old, rotting planks and rusty nails were assembled into a new ship. The spirit of an older item that is unlikely to be restored might be moved to a newer item of the same or vaguely similar type, through some emotionally important part of that item - a ship's bell or wheel, a gun's custom grips, a nameplate or commissioning plaque, et cetra - if the spirit wishes to, and/or is invited by a reasonably skilled caster.
The appearance of these spirits (or appearances, as many have more than one form, even if only one looks human) is most often determined by the thoughts of the people who are emotionally invested in it when the spirit forms, such as the designer, builders, and plankowner Captain, officers, and crew of a ship (even if the term isn't used, the first crew is still important to the thoughtform's 'birth'). These are themselves affected by a wide variety of things, but the ship's name and figurehead are significant, as much as the vessel's original purpose (and the language of the crew, as not all languages call a ship 'she'). For example, the tea clipper Cutty Sark, still working at sea on Steampunk Earth, and serving as a training vessel on Dieselpunk Earth, is named for Nannie Dee, a winsome young witch from the poem 'Tam o' Shanter', whose nickname came from the short ('cutty') nightshirt ('sark') she danced in. The figurehead is likewise made in her image. Thus, if the thoughtform of the ship were to manifest, she would most likely resemble Nannie Dee, whether or not her personality would be all that similar (if it is, she'd be inclined to manifest and dance with her crew, but would react badly, should an outsider see). The spirit's appearance and personality might change over time, or might not, but if so, there will always be at least strong hints of the original look and persona.
Loyalty is one important advantage of having a spirited item, even if the only intended power of the spirit is to resist psychic interference with normal operations. A well-treated and well-liked spirit will tend to be loyal to the item's owner(s) and user(s), and give any thief who isn't very skilled in spirit magics, and possibly some who are, a very hard time, as it seeks to return to it's master(s). At the very least, the magical aspects will often malfunction, or fail completely.