if the unit is icing up why would you tap it to see what the pressure is?
It's cooling, the issues sounds like it's not defrosting.
The parts list doesn't show a defrost timer
Or a main board. My guess it has a timer would be front and center under the front cover in the machine compartment.
Did you ohm out the defrost bimetals? there are two(according to the parts lookup)
GE page didn't have any info available.
Wonder if someone else can add info.