Your vehicle does not have a "standard" fuel pump relay. your fuel pump is controlled by a module called a CCRM, which has multiple control relays inside of it. Posting workshop data and pictures right now.
Mustang fuel pump "relay" description
Is your vehicle a convertible or a coupe? So i can post the location of the CCRM
It's a coupe
CCRM location - Coupe
It is called a "fuel pump driver module" in the component location chart
CCRM Wiring pin-out
Did you have any other questions or need any further information?
Is it possible for that part to fail & the actual pump still be ok?
yes. you would have to perform an electrical test at the CCRM to see if it is putting out voltage, or you could gain access to the fuel pump itself and see if you are getting voltage there
Thanks for everything. Hope I can find the part if it is actually the problem.