A githyanki fighter/mage
The term "gish" first appears in an official D&D product in the AD&D Fiend Folio (1981), p.43, where it refers to a githyanki fighter/magic-user:
2 'gish': fighter/magic-users of 4th/4th level
The githyanki did previously appear in White Dwarf magazine, issue 12 (1979), but according to RPG.SE user Carcer, we know that the term "gish" did not appear in that issue. It is likely an invention of Fiend Folio editor Don Turnbull, who, according to the Fiend Folio's preface, expanded upon some monster entries:
My own task has been quite a simple one - to select monsters for inclusion, to develop them as necessary and write the statistics and texts, to assemble the entries in coherent form and to produce the various tables.
The word "gish" is given an in-lore meaning in the Planescape sourcebook A Guide to the Astral Plane (1996):
Githyanki call those who are trained in both fighting and spellcasting gish, meaning "skilled". These talented individuals are rare and well-respected, often becoming leaders or other people of influence.
These men and women are multiclassed fighter/wizards – the only type of multiclass allowed to githyanki.
The name "gish'sarath" is given in the D&D 4e Dungeon Magazine #168 adventure A Tyranny of Souls, where it is said to mean "swordmaster". This construction originates in the D&D 3e era Polyhedron magazine, issue 159, p. 10:
For example, in the title gish'sarath, the apostrophe connects two independent units of meaning: gish, or "skilled", meaning a githyanki who uses both weapons and spells, and sarath, a modification of sarth, usually translated as "sergeant", a commander of the smallest military unit in the githyanki armies. It is pronounced gish´-sahr-ath´, with no vocalization of the apostrophy except perhaps a slight pause.
The rank "sarth" previously appeared in A Guide to the Astral Plane (1996), p.49.
Use of "gish" in a generic sense to refer to all fighter/wizard builds dates back to at least 2005, such as this post on rec.games.frp.dnd:
Well, the eldritch knight sees a lot of use in "gish" character builds, but consider the alternatives. How many builds have one level of spellsword for the spell failure chance reduction? How many builds have more than that one level? How many builds have that one level and go the distance with the eldritch knight?
This usage was likely introduced to D&D by fans of AD&D 2nd edition Planescape lore. While the term did appear in the 3e Manual of the Planes and 3.5 Monster Manual, it was only defined in those books as "multiclass githanki", meaning that the term must descend from the AD&D definition. There are probably earlier uses of the term that I don't have a source for.
As far as I can find, official sources used term "gish" to refer exclusively to githyanki, and its use to refer to fighter/wizard multiclass builds in general is particular to fan terminology most popular circa 1996-2007. According to a 2016 forum post, the term was used by fans in the AD&D 2e era.