There are two original Japanese-language abilities that have both been translated as 'Vanish'. The first is バニシュ [vanish], not to be confused with the spell Banish. The second is 潜伏 [senpuku] or 'concealment' in Japanese.
Final Fantasy IX
Type: Blue Magic, MP: 8
Learn from: ?
Other: Makes a party member vanish
Final Fantasy XII
Type: Arcane Magic, MP: 24
Element: Magical, Accuracy: always hits, Power: -
Target: allies/enemies, Radius: single, Range: 10, Charge Time: 30
Long Range: yes, Magick Evasion: no, Safety Nullify: no, Reflect: yes
Faith Effect: no, Recover MP: no, Remove Sleep/Confusion: no
License: Arcane Magick 4, LP: 50
Buy: 4,900 gil (sell: -)
Shop: Rabanastre (after Judge Bergan)
Effect: Gives Invisible status on the target
Other: バニシュ in Japanese
Final Fantasy Tactics
Type: Reaction Ability, Activation Rate: BRV%
Learn: Ninja (1,000 JP)
Effect: Gives Invisibility status in counter to physical attacks
Other: 潜伏 in Japanese
Explorers
Type: Time Magic, Equip Load: 30, AP Cost: 170
Target: area centered on caster, Power: -, Element: -
Cast time: ?, Recast: 70 sec
Learn: 5,000 CP, Specialty: Time Mage, Bard, Sage
Unlock: learn Blink and Reflect, reach main quest ★★★★ level
Description: Makes transparent allies within an area centered on the caster.
Other: バニシュ in Japanese
Airborne Brigade
Note that this ability has been translated wrongly as 'Banish' in FFAB. See that page for the data.
Category: Ability