The fridge will most likely only defrost every 12 hours anyway. If there is ice on the evap coils, ICE not frost, there may be a system leak.
When the coolant gets too low from leaking, a ball of ice will often form on the evap coils, otherwise, there should only be a fairly thin layer of frost on it until it hits defrost cycle.
Also need to test the defrost heat element for Ohms. No reading on the meter means bad element.

First of all, thanks to cletusT and denman for your inputs.

Denman, it was lots of ice, to the point that frozen foods were thawing.

Attached is the schematic diagram.

Based on this schema, i connected the loose black wire to Pin # 2.
In the old timer, there is a green wire that was connected to a side pin. This side pin does not exist on the new timer. I leave that green wire alone, unconnected to the new timer. It seems like a ground wire to me ?

I did not bother to cut the heater wires and test the heater element because that part is no longer available. Should I do that anyway ?

I double checked a few times yesterday and the timer indeed did not turn at all ( by comparing the marking i made on the gray knob? that is used for manually advancing the timer ).

For now, i set the temperature to the lowest setting and I haven't had to use the heat gun for the last 2 days to de-ice the evaporator coil.

In the first few days with the temp knob still set to high, there was definitely ice.

Again, thanks to all that responded.