It is vacuum operated, although can't say for sure on '04.
If noise is just after starting it could be timing chain cassette issue starting to show up, '04 was still using the older design I believe.
4.0l SOHC engines had a bad design on the timing chain setup.
Earlier TSB covered these models
Ford: 99-02 Explorer, 01-02 Sport Trac, Explorer Sport, Ranger
Mercury: 99-02 Mountaineer
*Engine - 4.0L SOHC - Rattle noise from primary chain drive area between 2K-3K RPM - Cold engine operation only
*Noise - Rattle noise from primary timing chain drive area between 2K-3K RPM - Cold engine operation only - vehicles equipped with 4.0L SOHC Engine only
Not sure if '04 would be effected
And your noise sounds different, just speculating