How did you check your refrigerant level?
The fan is normally tied into the a/c pressure switch, you need to verify your system pressures.

 

The only way I could check it and I am not sure if it is accurate was to take the gauge that comes with a recharge kit and see what it read.

 

That's only showing the low pressure side. Need to compare hi and low sides.
Has it ever been serviced?
Thinking you may have a sketchy expansion valve on the rear a/c. So restricted flow, maybe.

 

No I've not had it serviced. Would a faulty expansion valve explain why the condenser fan doesn't turn on? I was wondering if it could be the ambient temperature sensor or maybe the cooling fan temperature sensor.

 

Would a faulty AC pressure switch keep the condenser fan from coming on? I've got 12v at the relay but I do not have 12v at the fan itself.

 

Yes it can.
Is there a similar relay you can try in that spot to see if the A/C fan relay is toast.

 

I have swapped a few different relays to see if it was a faulty relay but there has been no change.

 

Have you seen this video?

 

I have, that's why this is so confusing to me. I have the 12v at the fuse block where the condenser fan relay goes. I have replaced the relay for the condenser fan, but still don't have 12v at the fan itself. That's what made me wonder if the AC pressure switch could somehow be keeping the condenser from getting the 12v it needs to turn on.

 

So you said it won't come on when the car is running, so does it ever come on?
Sorry I've got myself confused here, but the pressure switch can prevent a fan from coming on but I don't have the wiring diagram for a Sequoia.
The way I understand it the issue it may be the fan itself.

 

No problem. I'm confused too haha. The condenser fan isn't coming on at all and I've not been able to get a reading of 12v at the fan. I do have 12v at the relay.

 

you don't just fill the refrigerant to make it cold, you should read the low side at idle and then at 1,500 rpm. should be between 25psi and 35 psi. does it have separate front and back evaporators for the a/c?

 

Without the auxiliary fan the heat in the system isn't being dissipated. Adding more refrigerant can cause more problems since the pressure is already high without the fan and additional refrigerant is making it higher.

Your problem is the fan which should run anytime the A/C is on and you're at low speeds or idling. At higher speed the system should blow cold air front and back because you have natural airflow through the condenser and the clutch fan at higher engine speed can pull the heat out the condenser. You should take it to a shop for a proper diagnosis and fix.

 

first you should vac the system then weight in the right amount of freon over charging will have the your problem hope this helps