I will include some diagrams so you have a better idea what you are looking for.
The thermostat is located on the driver's side of the engine so I would rule that out right off the bat.
However, there are quite a few common components that can leak on the passenger side of the engine.
There are 2 plastic coolant elbow pipes that are common to crack and leak. One goes from the tensioner to the intake manifold and one goes from the tensioner to the engine. A picture will help so you can expect what to look for.
Next, the water pump is common to leak. Take a good look at the bottom of the water pump weep hole just behind the pulley. A small mirror will work to get a better look. Also inspect the gasket around the pump.
The lower intake has coolant passages in the corners of the cylinder head. These have been a notorious problem on the GM engines. Take a VERY close look at the corners of the intake for coolant leaks.
Not done yet. Inspect the 2 heater hose adapters that go into the tensioner assembly as well at the heater hoses running to the heater core.
Lastly, inspect radiator hose that goes to the water pump. This can leak.
Either way... A CLOSE VISUAL inspection is REQUIRED with a BRIGHT light to locate the coolant leak. Then, you can proceed with the repair process.
Most common to leak with this age of a vehicle is the water pump, the 2 plastic elbow pipes, and heater/radiator hoses.