Welcome to the forum
Keyless entry used to be run by the RAP(Remote Anti-Theft Personality) module.
Not sure on the 2010, On Rangers it was behind trim piece in rear of cab.
But could be in the Smart Junction Box(SJB) now, passenger side kick panel(fuse box), Ford moved most interior electronics there.
In early 2000's Ford switched many vehicles over to a CSM or BSM system for eyless entry, didn't rely on GEM type modules, auto locked doors when moving or when in gear(automatics).
Recently Ford also uses a VSM or Body Control Module(BCM), just FYI GEM was also called body control module, lol.
It's an alphabet soup of modules, wish car makers would just use one name and stick with it, like "keyless entry module", doesn't seem that complicated to me to do that, but I guess you can charge more for a Remote Anti-Theft Personality Module
Just found this: 2010 Ford Ranger XLT Were is the VSM module & how do I
Seems Ford is calling it the VSM