I had a similar thing happen on our other '99 Burb 350. Dad and I were planning to replace the belt and tensioner and do an oil change. So I get under it to put the new belt on(I hadn't come up with my trick or using small spring clamps to hold the belt onto the crank pulley, to keep it tight and in place while you get the belt routed around the other pulleys). And I'm under the front of the engine...and I see the dreaded orange pee.
So... ended up replacing the water pump and bypass hoses, upper hose, lower hose, while we are in there, look at the timing set, yeah it's got slack after 175K on original parts, gotta replace the timing cover (no aftermarket ones available then, so got a $60 OEM one from the Chevy store), had to drop the pan to get the cover off, had to jack the motor up to get the pan out.....
A job that was going to be a couple of hours one afternoon, ended up taking almost a month. I was working more then so I could only wrench on days off and weekends....