I will start by saying I have close to no experience whatsoever with vehicles in general, and this noise may just be the sound of the truck itself. In the video I included you'll hear the noise throughout the whole video. It is a low, relatively quiet whistling noise, and it is constant the whole time the truck is running. It does not go away or get quieter, but does ever so slightly fluctuate pitch randomly.

It is a 1999 2wd XLT Ext. Cab Short bed