Yea thats another very posable solution!
      One way to find out is to use piece of solid bar, with the engine running touch the bar to the pump then put your ear at the other end of the bar if something is wrong you should be able to hear the amplified noise. This is how I check for bad bearings, it becomes clear quickly which parts are making the most noise.
      BE VERRY CAREFUL NOT TO TOUCH ANY MOVING PARTS WITH THE BAR! THIS IS VERY BAD......TRUST ME!!

HAHA  THAT WAS A BAD DAY!  

my girl squeeks. thats how she tells me she loves me!  

I have a 2000 Grand cherokee laredo 4.0 that is doing same thing (high pitched whistle). It has been going on for a very long time, does it most of the time in colder weather especially after you drive it a couple miles sometimes less but then when you get out to listen for it by the time you get hood up most of times it stops, though it was fuel supply line but finally got a hose  and it sounded like it was coming from power steering pump, it does it worse when sitting @ stop light idling then when you pull away it quiets down. I heard they have orifices in them that could get partialy clogged,don't know if this is it though don't have any vaccum hoses around that area.
My wife refuses to drive it any more till I get it fixed so if anyone knows or has tried this fix let me know PLEASE!!!  

I got the EXACT same issue. LOUD whistle when i idle. giving it gas makes it go away and letting off of the gas it starts back up and while it does the whistle it runs really rough and almost dies at stop signs. Starts about 3 minutes after I start the jeep and (sometimes) goes away after I drive around for a while & when the whistle stops the jeep runs perfectly smooth.
It's for sure not a belt or water pump.

It seems to be coming from the carb area. It is a high pitch whistle almost like a tea kettle but 1000 X louder.(you can hear it from blocks away) My carb is about 1 year old and the noise started when it got cold out. replaced all of the gaskets on the carb yesterday and that didnt help. Gonna mess around with it again this weekend.  

i got another problem with my jeep, is there any reason why the inside of my roof has condensation on it? i dont really know why it happens, any help? thanks, oh and for some reason the squealing noise went away for now, it hasnt done it the past few times ive driven my jeep.  

Deadfred, it seems like you have a vacuum or intake leak.  When the engine is cold, and the choke is closed, it will make any intake leak worse than when its open.  Essentially, your motor may be running lean due to the leak because the carb. doesn't see all the air coming in the engine and can't compensate with more fuel. If you have an inline, you can take some grease and put a small bead around the intake port at the head (i know its a pain).  It should seal for a short period, enough to tell if thats what it is or what cylinder.  If its real bad, it may suck the grease in and that will give you a sign.  I should mention don't let the engine run for too long, the grease may thin out and run down and do this when its cold.  

I have kind of the same problem. I thought I would post what I have tried so far to figure out what is causing it.

2004 wrangler, 4.0 automatic.
I have a loud high-pitched noise that comes and goes. It will make the noise while at idle and while driving. When I give it gas, the noise “throttles” up then goes away. When I let off the gas the sound comes back. It will start to make the noise with in a few blocks from home. Sometimes the noise will go away for 10 – 15 min then start up again. It does seem to be worse the colder it gets outside. The engine runs good. There are no other problems other than the very annoying noise.

I replaced the belt and tensioner, but it doesn’t really sound like belt squeal. I took it to a shop that I trust. They ran it with out the belt, it still made the noise. They did a test using smoke to try to find any vacuum leaks. They didn’t find any. They pulled off the throttle body and replaced the gasket. It is still making the noise. I read a post on another form from somebody else that has a similar problem. The advice given was to check the air intake. I’ll give that a shot tomorrow.  

like Jeep420 said(by the way great name) water pump might be going and check your power steering pump as well.
try taking a long breaker bar or pry bar and while your motor is running put the bar on a pump and put your ear on the other side and listen for a squeel, that should help pinpoint your problem.  

Thank You. It's an '89 yj by the way, straight 6. I will try that this weekend. Got the flu so didnt get to mess with it yet. Looks to be fairly nice out this weekend though. Any other way to apply this method in warm weather?

OH! It has also been whistling even in the recent warm weather. Don't know if that matters?  

I have a Jeep Wrangler 1991.  The Serpetine belt broke and we replaced the belt.  My husband cleaned the engine with GUNK cleaner.  The belt developed this annoying squeal.  We were told to replace the idler pulley, so we did, still squeals.  So we replaced the belt again, still sqeals.  Tightened the belt still squeals.  I had a mechanic check it out and he said it is definitely a belt squeak.  He listened to all the pulleys, altenator, power steering etc.  he said the noise is coming from the belt.  Any suggestions on what I can do, I have heard of squeakey clean but this is ridiculous.  

If the mechanic said its the belt, have him put a new one on. and when it still squeals go back and ask him whats going on!!  

Try replacing the fan clutch. I had one on my '99TJ start squeaking on me and it was driving me nuts trying to find it.  What gave it away for me was what looked like a seal blown out @ the shaft, tried turning it and felt like it was catching on something internally.  

Ive come across belt squeel caused by too much head pressure in the AC system.

  Pull your belt off and inspect each pulley for wear...spin them  and listen to them to make sure they roll smoothly, you dont want any play in them....if there is play  replace it. Also check the grooves in the pulley where the belt rides, make sure there is no rubber stuck in grooves from previously cheaper belts   Parts now are generally cheap, If you suspect an idler pulley or a tensioner pulley or an altenator replace it....if its the water pump  same applies, power steering pumps have some in and out play.. as long as they dont leak  its ok    

And yes I too recomend the Good Year Gator Back...a very fine belt indeed.      Hope that helps a little.

Preventitive Maintenance is what its all about!