I'm having a similar issue on my 97' blazer. I've got a decent leak coming from somewhere near the rear of the engine. When the truck is off, there is no leak, or so slight that I can't notice it. But once the engine is on, it leaks badly. I'm not a mechanic by any stretch of the imagination, and I tried to trace the source of the leak. I checked any and all hoses and lines that I could reach from the top-down, and they were all dry. Then, I checked any and all lines/hoses I could reach from the bottom-up...again all were dry. The leak seems to be coming down from the engine onto the transmission...but, only on the drivers side. My father-in-law has been trying to walk me through different checks for heater core, freeze plugs, busted hoses but I'm lost. Any help would welcomed.

 

Your problem is most certainly a LIM (lower intake manifold) gasket leak. For further information into this fairly common problem, please use the search feature.