Welcome to OEM fuel pumps. You probably need a new one. Unless you have a lot of upgrades or are planning upgrades, I would replace it with the high pressure version of the stock displacement pump. Meaning: If the stock pump is 88 liters per hour then get a high pressure 88 liter per hour pump made by "Walbro". BBK pumps and many others are re-branded Walbro pumps but you want to be sure to avoid the parts store Chinese knock-off.
If you cannot positively identify a Walbro pump then purchase a replacement from the dealership. I would hazard to guess that any of the Mustang parts stores on-line have these pumps (I'm sure of it). Check the vendor forum for discount codes.