It does sound like air. This is out-there but did you try blowing the horn a couple of times?

 

This almost sounds like the horn is partially on.....strange!!

 

My 2000 blazer made that exact sound when i had a big vacuum leak between the upper intake and the top of the spider injectors (top meaning where the fuel lines go) so i too would be checking for leaks. Try pushing on your upper intake manifold and try wiggling that top part of the injectors to see if the noise changes. That's the only way i stumbled across where mine was making the noise. Other than that check vacuum lines like someone already suggested.

 

skid guard or something else maybe rubbing on the crankshaft pulley? also ive heard similar noises when the transmission inspection shields rub the flex pipe but i dont think s10s even have them

 

Sounds like either the altenator or ac unit.Unplug the ac and see if it goes away.

 

I believe he said it still makes the noise even without the belt on.

Spray your engine down with a garden hose and watch when and where the noise stops....just a thought.

 

Ok so here is the update:
-nothing to do with crankshaft or underneath rubbing.
-located noise more towards top middle of engine.
-found a stray vacuum hose off by itself unconnected to anything by the brake reservoir, cant find where it goes but have a pic.
-also took off air intake to help find sound and noticed there is a hole in the carb (or whatever its called where the air intake meets the engine. Is it supposed to? noise is super close around it somewhere.
-not the horn, the AC, or anything with the transmission.
-and once again nothing to do with belt related options.
here are the pics.

 

That looks like your brake booster line and that would definitely create a noise like in the video. It plugs into the round black canister attached to the driver side of the fire wall and to a nipple on the back driver side of the upper intake manifold. Its in the back right corner of your first picture. You can't really see it tho in that picture

 

anyway you could snap a pic for me???

 

That vac line was rotted on mine also. Replaced it when I had engine apart doing head gasket.