Camshaft position Sensor.
SOHC does not have moving parts. They mounted this on the left valve cover. This setup uses a magnet to detect a special tooth on the camshaft.
The DOHC(pushrod) 4.0 and the 5.0 V8 engines are modified engines that have been used for a very long time. Both used to have a distribitor. But our modified versions do not. They started using Coil Packs, which are a bit more reliable. Instead of just pluging the hole where the distributor was they figured that it was the best place to put a camshaft position sensor. The camshaft position sensor tells the computer how to synchronize the fuel injectors with igniting the sparkplugs.
Most people think "It is just a sensor, so there is no moving part. However, the actual sensor sits directly on a drive unit that rotates with the camshaft. The drive unit looks just like the bottom of the old distributors. The top of the drive unit rotates around a magnet inside the sensor. Like any moving part they will wear out and need replaced. It is the most common ghost "bird chirp" on the Explorer.
The 5.0's camshaft position sensor is located under the coil packs and on top of the waterpump. It can be purchased as two seperate components. The camshaft position sensor($35) and the Camshaft synchronizer assembly($100).
The DOHC's camshaft position sensor is located on the rear of the engine block. It is a little hidden, but look hard and you will find it. It can be purchased as two seperate components. (Before 1996 the sensor and drive unit are one piece.) After 1995 the camshaft position sensor($35) and the Camshaft synchronizer assembly($100).
You will also need a special tool that is hard to find local. But online just do a search Ford camshaft tool and you will find it.
Haynes manual does a good job at explaining how to replace it (It sounds hard but is way overrated). Just take your time and have patience.
A shop will charge over $300 and any other parts and labor they think the squeek is coming from.