I have a GE TPS24BPDABS refrigerator and needed to repair some cracked water supply lines. I think I may have switched the 1/4" lines when I reconnected them to the valve because the water dispenser ran without being pushed on. I have tried to find a schematic as to what supply lines connect to which openings on the valve (it is the double valve) and am unable to locate that information anywhere. Any help would be appreciated.

This sound more like a failed switch/valve than anything about the lines. Does the water run continuously when supplied?

Only two ways to do it. If you have lines connected to correct valves everything works properly. If you have them backwards you should get water in the ice maker tray when you press the chilled water leaver. You would also get water out the chilled water dispenser when the ice maker calls for water. Reverse connections.