I believe the jineta subject is quite more complex than initially thought so the best is to pile up all the relating info.
This is an interesting start even when in Spanish:
http://www.alhambra-patronato.es/fil...sa_nazar__.pdf
There are several archeological remnants usually not mentioned as ginetas, for example this islamic sword found at Guadalajara (the gilt one).
For me, the closest relatives to the Nasrid jinetas come from the Mamluk State. And the Mamluk weapons come from Syria. And the Syrian weapons are derived from Bizantium.
Interesting pictures in an article by Yotov:
https://www.academia.edu/2328824/A_N...1th_CENTURIES_
A not anymore extant Jineta was painted by El Greco. You can compare it to the San Telmo Gineta and a Mamluk banner...
You have mamluk swords with low quillions and others where the hilt surrounds the sheath mouth. Spheric pommels seem to be a characteristic of some mamluk and bizantine swords...
We can go East to Xian an Tibet as well...