Changed the TFI, Mustang still shutting off after about 10 minutes

PIP Sensor functionality, testing and replacement:
The PIP is a Hall Effect magnetic sensor that triggers the TFI and injectors. There is a shutter wheel alternately covers and uncovers a fixed magnet as it rotates. The change in the magnetic field triggers the sensor. A failing PIP sensor will often set code 14 in the computer. They are often heat sensitive, increasing the failure rate as the temperature increases.

Some simple checks to do before replacing the PIP sensor or distributor:
You will need a Multimeter or DVM with good batteries: test or replace them before you get started.. You may also need some extra 16-18 gauge wire to extend the length of the meter’s test leads.
Visual check first: look for chaffed or damaged wiring and loose connector pins in the TFI harness connector.
Check the IDM wiring – dark green/yellow wire from the TFI module to pin 4 on the computer. There is a 22K Ohm resistor in the wiring between the TFI and the computer. Use an ohmmeter to measure the wire resistance from the TFI to the computer. You should see 22,000 ohms +/- 10%.
Check the PIP wiring - dark blue from the TFI module to pin 56 on the computer. Use an ohmmeter to measure the wire resistance from the TFI to the computer. You should see 0.2-1.5 ohms.
Check the SPOUT wiring – yellow/lt green from the TFI module to pin 36 on the computer. Use an ohmmeter to measure the wire resistance from the TFI to the computer. You should see 0.2-1.5 ohms.
Check the black/orange wire from the TFI module to pin 16 on the computer. Use an ohmmeter to measure the wire resistance from the TFI to the computer. You should see 0.2-1.5 ohms.
Check the red/green wire; it should have a steady 12-13 volts with the ignition switch on and the engine not running.
Check the red/blue wire; it should have a steady 12-13 volts with the ignition switch in Start and the engine not running. Watch out for the fan blades when you do this test, since the engine will be cranking.
If you do not find any chaffed or broken wires, high resistance connections or loose pins in the wiring harness, replace the PIP sensor or the distributor.

The PIP sensor is mounted in the bottom of the distributor under the shutter wheel. In stock Ford distributors, you have to press the gear off the distributor shaft to get access to it to replace it.

To remove the gear, first you drive out the roll pin that secures the gear to the shaft. Then you get to press the gear off with a hydraulic press or puller. When you go to press the gear back on, it has to be perfectly lined up with the hole in the gear and shaft. I have been told that the hole for the pin is offset slightly from center and may require some extra examination to get it lined up correctly.

Most guys just end up replacing the distributor with a remanufactured unit for about $75 exchange
PIP problems & diagnostic info
Spark with the SPOUT out, but not with the SPOUT in suggests a PIP problem. The PIP signal level needs to be above 6.5 volts to trigger the computer, but only needs to be 5.75 volts to trigger the TFI module. Hence with a weak PIP signal, you could get spark but no injector pulse. You will need an oscilloscope or graphing DVM to measure the output voltage since it is not a straight DC voltage.

See http://www.wellsmfgcorp.com/pdf/counterp_v8_i2_2004.pdf and http://www.wellsmfgcorp.com/pdf/counterp_v8_i3_2004.pdf for verification of this little detail from Wells, a manufacturer of TFI modules and ignition system products.