Hello and welcome to Just answer.com, Super mechanic here. About your vehicle.
It may be the "O" ring seals for the coolant pipe that runs from behind the water pump to the back of the engine, (#14),
When they leak, coolant will come out from the rear of the intake manifold. To get at them, the intake has to come off.
Since I'm going to let the Mitsubishi dealer change out the water pump and Timing belt, I only removed the intake manifold and replace the hoses and thermostat and there was a new ORing that I did replace with the thermostat per the repair manual.
I can not start the car, because I have the intake manifold removed.
I see no leak at the (new) thermostat or (to be replaced by dealer) water pump.
So what you suggest I do?
I'll work with your information, I'm an engineer by training and understand the design of American cars, the Eclipse is my wife's car and I must say that the Japanese design is totally new to me!!