Here are your parts
Replacement parts for FRG FRT18LN5BW0 | AppliancePartsPros.com

Here is the parts breakdown
ftp://ftp.electrolux-na.com/Pr.../Anderson/5995370029.pdf

And here is a wiring diagram
ftp://ftp.electrolux-na.com/Pr...F/Anderson/240379007.pdf

Could be the defrost timer, defrost thermostat or the defrost heater.
Looks like the defrost timer is at the top of the fresh food section, if you look up you should see a hole in the cover which will let you manually turn the defrost timer cam.

Remove the evaporator coil cover at the back of the freezer.
Turn the defrost timer cam with a screw driver till the compressor, the compressor fan and the evaporator fan go off. You are now in a defrost mode. Note the cam only turns one way.
Check to see if the defrost heater is on.
Be careful do not burn your fingers.
Also the defrost thermostat must be frozen as it shuts power off to the heater just above freezing.
If the heater goes on odds are high that the timer is shot.

If the heater does not go on then it is likely either the defrost thermostat or the heater. Note this does not totally rule out the timer as it's contacts may be shot.
Measure the components with a meter.
Defrost thermostat should be 0 ohms when frozen.
Defrost heater should be around 35 ohms.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.

I am going to replace the defrost thermostat, which was one of the 3 suggested problems and hope that this will take care of it.
That is all that is left in the defrost circuit. Only other thing it could be is a bad connection somewhere.

One thing though...There was still a noticable amount of frost build-up on the bottom half of the evaporator and I did not thaw it prior to restart after heater and defrost timer installation. I was wondering if it was possible that the heater could not get all of that defrosted in the allocated defrost cycles, which caused it to re-ice even further.
Just a couple things.
Did you have the evaporator coil cover on, it must be on to get a proper defrost.
I assume the freezer fan is running OK and shuts off during defrost?
The heater is at the bottom so the ice on the bottom should melt first.
This is also the reason the thermostat is at the top, so that the entire evaporator coil is defrosted before it switches off.
Note: I always manually defrost the system before installing the new parts so that may have been the problem.

The icing up just at the bottom does concern me especially if this is where the freon enters the evaporator coil from the compressor. This can be an indication of low freon. Once you get it defrosted, check that the coil gets a fairly even coating of frost after it runs for an hour or so.
The below may help see the example pictures
http://www.applianceaid.com/frig_notcold.html