Hello Meir,
If water is appearing on rear wall in fridge, this is a good indication that condensation tube is clogged.
I've had this same problem in the past, I'm not familiar with all Models, but the one I worked on had a plastic tube mounted inside rear. It was stopped up after many years of service with thick "GunK", in the freezer was a drain hole (rear but in freezer), try pouring hot water in this tube and/or syringe or something to apply a little pressure, if it doesn't open easily--you may have to use a diluted bleach solution and let it soak. This tube runs from top to bottom of refrige--to a evaporator pan beside condenser coils.
Hope this helps
In Christ,
Walt, October 2008