Freezer with defrost issues - dripping water inside.

I’ve been trying to figure out an issue with our freezer, but haven’t had much luck so far. The freezer is supposed to be frost free. When I open the freezer, on the top side of the door there is either ice that’s frozen solid or ice that’s dripping water. When it’s dripping water, the temp inside of the freezer doesn’t seem cold enough (melted ice create, popsicles, etc). Changing the temperature doesn’t seem to have much of an impact.

My guess was initially that I had a door gasket issue, so I replaced that. It didn’t seem to make a difference. I then started to evaluate the defrost system. I’m definitely not an expert at repairing freezers, so I haven’t made it very far. I’ve double checked that the coils do not get frozen. They just seem to get a normal amount of frost on them while it’s cooling. The defrost heater kicks on and gets hot, so I’m guessing it’s not an issue with the heater. I initially thought it was an issue with my defrost timer, but I guess I don’t have a defrost timer. When I look for parts on appliance parts pros, it shows me a diagram for a model that’s not an exact match.
http://www.appliancepartspros.com/partsearch/model.aspx?model_id=5120746
It shows a defrost timer in the diagram, but I don’t see it anywhere, and the circuit diagram on the back of the freezer doesn’t show one. Is it possible that I don’t really have a defrost timer? If I don’t, does this issue sound like an issue with my defrost thermostat instead? Any ideas on what else it could be causing the ice and too warm temps?

Thanks a ton for helping a freezer repair newbie!

Ice buildup on top of and inside a freezer door has to be a gasket issue… Even after replacing it and ice buildup returns then there’s still a gasket issue… And if the freezer temp ‘seems’ or ‘feels’ like it’s not cold enough then place an accurate thermometer inside the freezer and monitor the temp over a day or two… Don’t go by feel, look at accurate temps; a freezer should be around zero to 5 below, 5 above is not unusual as long as the compressor kicks on shortly to bring temps back down to zero or below… Post back with more info to possibly nail down the problem and YES if your fridge is frost free then it has a defrost timer builtin somewhere… cheers kooler