Waterpump housing is probably cracked. I thought that it was an issue on the T400s that were corrected in the T800s. but I guess not.
I had the exact same thing go wrong on my 1995 Silverado (it had about 110,000 miles on it at the time). I was a slow leak and put water in the tank to ensure that it didn't overheat until I brought it in to be repaired.
$250 to repair roughly if you go through a shop. GM dealer may charge slightly more but they are less likey to screw it up.
It's a very common part, and you should be able to get it easily.
It's not that difficult to do it yourself if the design is similar to my T400 truck. I'm sure that GMCSonoma or Shadams can contribute to the correct procedure. You can buy the part for cheap from the GM parts website or through a dealer. Johnny P seems to have given you good advice on the procedure that sounds really familiar.