Weird electical problem

Bad or missing power ground. Some people think it is just a ground, it doesn't do anything important. In automotive circuits, the ground is the return path back to the alternator or battery.

The secondary power ground is between the back of the
intake manifold and the driver's side firewall. It is often missing or
loose. It supplies ground for the alternator, A/C compressor
clutch and other electrical accessories such as the gauges.
Any car that has a 3G or high output current alternator needs
a 4 gauge ground wire running from the block to the chassis
ground where the battery pigtail ground connects.
The 3G has a 130 amp capacity, so you wire the power side
with 4 gauge wire. It stands to reason that the ground side
handles just a much current, so it needs to be 4 gauge too.

The picture shows the common ground point for the battery & alternator

Picture courtesy timewarped1972

if i remember correctly, that year stang has a voltage regulator for the I/P. if it goes out it will cause that type of problem. it's located on the back of the I/P.