My name is Peter. I am a retired field service refrigeration technician.
Ok, It may have been the water bottle. But, you have an old unit.
So, lets check it out once more.
1.) After time, from the heat, the plastic tubing for both your water lines to the water dispenser and ice maker will dry rot and crack.
Check: Pull your unit out. Have someone draw a glass of water from the water dispenser, while observing in the back both the water supply valve and the larger plastic tubing going to the water dispenser. Is there a leak when pressurized?
2.) Wait for when your ice maker fills and observe the smaller plastic tubing. Does it leak under pressure.
Part Number: Substitution: 4387492 Cost: $10.00
3.) Drain Pan - This too will crack over time do to heat. Pull your unit out so you can get behind it. Remove the lower back cover.. There are about 8 screws easily removed. Observe the drain tube from the under body of your refrigerator and the black drain pan where it empties. Observe around the drain pan. Are there and brown or dark stains on the floor? If so, then you have a cracked drain pan.
Repair: Unplug the refrigerator. The compressor and surrounding copper tubing prevent you from replacing the pan. When I was in the field, I would take duct tape and seal the cracked area. Then, I would cover the duct tape and surrounding area with a high temp silicone adhesive.