I'm going to assume this is a 3 valve single over head cam (SOHC) 4.6 with a "drive by wire" throttle. This could be:
- The throttle body itself
- The throttle position sensor (the right foot pedal position sensor).
If looking for an educated guess the problem is in the throttle body. But it would help to have some more information to go on such as a DTC code. There are two position sensors inside the TB. The PCM goes into to limp in mode when the sensors disagree.
Disclaimer. I don't own a 2005+ Mustang. But I do work on a 2005 F150 with the 3V SOHC 5.4 drive by wire. So I do have some understanding of the system.
For cars with the advanced systems such as "drive by wire", IMO it's very hard to correctly trouble shoot without access to an ODB2 scanner. Something that can access, monitor, and graph operational PID's. An ODB2 scanner can also make short work of question like, "what is the sensor's value?". Graphing makes it possible to compare the values over time. Important when dealing with "soft" faults.
Here's some information on an affordable Windows based unit.
ForScan ODB2 scanner w ELM327 USB
https://www.stangnet.com/mustang-forums/resources/forscan-odb2-scanner-w-elm327-usb.57/
With this software it's very easy to graph the two throttle position sensor values and see if they diverge. Of course the problem could be obvious from the DTC code.
Here's some information that might help you to understand the problem. The video is by a very good Ford tech FordTechMakuloco
Ford Electronic Throttle Body Failures
View: https://www.youtube.com/watch?v=FDpUo3UPmto
Finally this thread was posted in the 1996-2004 model year section. There maybe people in the 2005+ MY section of the forums better able to help.