I can’t find it on google or ah. Did I imagine it?
I think you did… I think you’re thinking of the Grand Expedition Yak that lets you transmog.
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There is no mobile barber yet.
As Monzastrasza stated above, There is currently no mobile barber in the game at this time. If you are looking for a barber, You need to find one in a major city.
However, If you’re looking to change your transmog appearance, Then you’ll want to purchase the Grand Expedition Yak in Kun-Lai Summit.
If you are looking for a mobile Auction House, Then you’ll want to find a player that has the Mighty Caravan Brutosaur mount as you can no longer purchase it from the vendor that used to sell it in the Battle for Azeroth Expansion.
Cheers! 
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It’s like a consumable item. Maybe made by engineers? It’s not part of a mount.
As far as I’m aware there is no item made by the Engineering Profession that allows players to use the barber shop feature. Engineers however can create items that can allow players to obtain some cool items.
Such items include Blingtron 4000, Blingtron 5000, and Blingtron 7000. However, Note you can only loot one of those types each day on each character you use to obtain their gifts. Also, If you get a gift from one of those, You cannot get a gift from the other two for that day.
Other items Engineers can make include Jeeves which allows the Engineer to access their personal bank. It also allows players to repair any gear they have equipped.
Last item I can think of is the item Ultimate Gnomish Army Knife that has a chance to resurrect dead players in your group.
That’s not what they asked.
They asked about consumables that are like barber shops.
There isn’t a barber shop consumable.
There is only Deployable Attire Rearranger and Interdimensional Companion Repository.
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I was mixing up the attire aranger. Darn.
Well there is that Toy from Horrific Visions that gives you a shaved head if you click on it.