Is this hose supposed to be here?

This hose and assembly is located on the rear of my auto transmission. I found the hose dangling and assumed it attached to this black box in the picture. Is this correct and what is this? Thank you in advance!

 

It is a vent / breather hose the for 4x4 actuator (the black box). That works in conjunction with another similar actuator on the front axle to switch the truck between 2Hi, 4Hi, and 4Lo.

It is correct as you have pictured.

If you found it disconnected, you may want to test the 4x4 system is still operational and keep an eye on it over time. If any water at all gets in either one of those actuators it can cause issues with the electric motor and switches inside.

 

Random picture when I Googled "Tacoma transfer case":

 

Yes, it's the vent hose for the Transfer Case Actuator, pretty common for them to get dry rotted and fall off.
If the hose is bad replace it because if it falls off dirt and water gets in the actuator and destroys it.
https://www.tacomaworld.com/threads/4wd-system-operation-help-thread.742420/

 

Thanks for the quick response, im actually on the beach right now with 4x4 engaged with no issues.

 

Do you know the part number for that hose by any chance? Mine was splitting so I cut it and put it back but it’s kinda stretched now. That’s one of those, I’ll get to it eventually things lol

 

I do not, if it was mine I'd probably just find some vaccum hose that was the right size and replace it with that.

 

This might be the hose - 90447-08175. I did the same as @hx989 .