Some of the Ford motors have a hard to locate chirping noise that comes from the Cam Position Sensor when the bearings in it go bad, not sure if it applies to the 4.0 SOHC or not though. My 5.0 V8 has developed a chirping recently, and seeing as how the belt, tensioner assembly and idler pulley are all new, I believe it may be the culprit. I need to pull the belt off this weekend and see if the noise is still present.
Basically, in the 5.0 V8, the CPS is like a distributor minus the top rotor and hat, and it fits into the block where the distributor used to and meshes with the gear on the camshaft, as well as drives the oil pump. The actual 'sensor" is then mounted at the top right where the opening in the lower intake manifold is, and it provides the ECU with timing info to fire the coil packs.