The back door doesn't open. I hear a clicking noise when I push the button, but the door won't unlatch. It is a 2012 Ford Escape.
The problem is the latch actuator broke and needs to be replaced. The replacement part number is 9L8Z-7843150-B. I found genuine parts on Amazon for ~$100 or a generic part on Ebay for ~$50. This part will fit 2010-2012 Ford Escape & Mercury Mariner. Here's a video on how to do the repair: https://www.youtube.com/watch?v=BKXGgQYXXO4
I have had the same problem with a 2001 Escape. Remove the actuator assembly from the tailgate, then disassemble it. If it looks mechanically fine (no broken plastic parts) then likely it is just the motor and you won't need the whole assembly. Test with a multimeter or 12 volts on the terminals. Motors are under $5.00 from Ebay or Ali in 2019. Made by Mabuchi, they come in various sizes and shaft configurations. Buy the one with shaft lengths and motor body size closest to yours. If I remember rightly the part number is stamped on it which makes finding one easier. You won't find a motor with the little press-on drive widget on its shaft and which slots into the plastic gear train.
The one on your old motor comes off but be careful not to shatter it. It is a tight fit on the shaft but it does come off. Fit it to your replacement motor using a vice, and be sure to compress the shaft end to end in the vice rather than the motor body so you are not putting stress on the motor. Then fit the motor back into the actuator housing and fit the little plastic bits back where they came from. It's all straightforward and obvious. Locking and unlocking the tailgate is just by polarity reversal, so make sure the mechanical parts are in the right position before sealing it up again and fitting back onto the tailgate.