Based on where the water was coming from I suspected the condensation from the evaporator was not draining properly. I pulled off and cleaned the drain tube in back and noticed lots of sediment from corrosion. Cleaning the tube did not fix the water accumulation problem, so I did some research and determined the evaporator drip pan was probably the cause. Replacing it was straight-forward, except for the fact that a block of ice had formed on the refrigerant lines, freezing parts including the evaporator cover in place. I was being very careful not to damage anything so it took some time to get the covers off. Regardless, I ended up lightly damaging the plastic evaporator cover and the styrofoam in the evaporator fan assembly, but managed to fix them well enough with some silicone sealant. The removed evaporator drip pan was highly corroded with dozens of pinholes. Fridge is now working great, and so far no dripping water or ice build-up. I did make a mistake causing minor damage to parts, but if I had to do this again I think it would be quick and easy. Hoping this 18-year-old fridge makes it to 25! My part was shipped quickly and the price was good compared to the competition.