Excess ice in top-freezer part of refrigerator

We have an Amana model, purchased in 1991.
The top freezer in the model (i.e., the refrigerator has the freezer on top) often gets a lot of ice in it, typically hanging from the front top edge of the compartment of the freezer ceiling.
The model is otherwise sound. It maintains a good temperature in both the freezer and refrigerator. Occasionally water will leak into the refrigerator compartment, and some work on opening up the drain tube fixes that.
My questions are:
1. What is causing the ice build-up and how do I stop it? It's not heavy ice, just more than the none that I'd expect. I suspect if I collected and melted it all, it would amont to 3-5 tablespoons, tops.
2. How do I access the drain tube in the model? Every time I've had to clear the tube, I've done so by emptying the freezer, pouring a lot of very hot water into the freezer compartment, then thoroughly mopping up. There must be an easy way to access the tube itself from inside the freezer or refrigerator.
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trader-of-some-jacks wrote:

Hi, Don't block the air flow between two sections(freezer, fridge). Maybe fan is seized? Or defroster is acting up?
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One thing I came across in my research was vacuuming the coils. The coils under the refrigerator were almost invisible amongst all the dust. So I game them a thorough cleaning. I don't understand how dirty coils can contribute to ice buildup in the freezer, but let's see if that works.
Still hoping for an answer on how to access the drain tube in the model.
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