Tailgate lift is usually a word the Australians use. There is no wrong or right when it comes to Lift Gates.

There is also no reference as to which spelling is correct when it comes to the US word/s lift gate, lift gate. What’s funny is even as typing this article spell check with Microsoft is telling me lift gate is spelled wrong. Once I change it to lift gate it then is very happy. If you go to dictionary.com you will see it has no definition of lift gate, but gives you a definition of one whole word lift gate. It then gives you a reference to the 1945-1950 keyword lift + (tail) gate. The only definition it has for lift gate is “hatch”.
Many lift gates fall into many categories. I really do feel tailgate lift would be the appropriate word, however I usually never hear that term unless it is someone from Australia.
The Webster Dictionary does not have any definition for any of the lift gate combination!
Tailgate lifts can also get confused with the kit that transforms the original tailgate into a hydraulic lift making it easy to open and shut a regular tailgate.

Check out the Classic Lift gates from Kortia.