I have resolved my issue with the freezer alarm not working, and its location in my model.
The freezer alarm IS located in the control box area as suggested by RegUS_PatOff. My user guide says the same thing. Previously, when I took the control box off, I did not remove the thermostat from it to get a better look, because of the short length of the thermostat coil. This was my first time fixing the freezer and I didn't want to mess anything else up. Plus, I didn't even know what it looked like.
So today, I took a better look and saw the alarm tucked into the back, then decided to remove the thermostat, and there is was. I have included photos of it for future reference, and here are the steps I did to replace it.
1. Shut off thermostat, then unplug freezer from the AC line.
2. Remove the control box housing the thermostat and alarm switch by removing the two screws that are recessed at the bottom of the control box.
3. Carefully tilt the box forward enough to see the thermostat, but don't force it or you will damage the coil going into it. Remove the thermostat knob.
4. With a small blade screwdriver, gently pry the plastic clips that hold the thermostat, then you can lift it out of the mounting bracket and set the thermostat to the side.
5. Now you can rotate the control box froward and see the alarm in the rear. The color blends in with the rest of the box, making it hard to see without the thermostat removed.
6. Make a color code diagram of the alarm switch leads as they attach to the alarm switch. The center leads of the switch stay connected. Only the 4 end leads get connected to the alarm.
7. Pull off the lug leads one at a time, not all at once, each time replacing them with the good alarm leads of the appropriate colored wire.
8. Remove the black clip thermocouple sensor lead from the mounting post that the front mounting screw of the control box screws into. The clip is there to allow the sensor to monitor the freezer temperature and trigger the alarm if the temperature goes 10 degrees above the set temperature.
9. Before removing the two mounting screws from the bad alarm, test the new one by plugging in the AC power and flip the alarm switch to TEST. No need to turn on the thermostat. You should hear a "binging" sound. If so, then you can unplug the AC and remove the mounting screws from the bad alarm and mount the new one. Put the screws into the alarm first, just slightly coming out of the mounting holes, then mate them with the holes in the control unit inside base.
10. Carefully put the thermostat back into its holding bracket. Put the knob back on.
11. Position the entire control box so the two mounting screws fit securely into the screw posts.
12. Plug in the AC power, set the thermostat, test the alarm again, and you should be back in business.
Thanks to everyone who had input on this post. I think we all learned you can never trust wiring diagrams, parts lists, etc. to show exactly where things are since there are so many variations of similar appliance models. Experience wins all the time, and it's a snap doing it the SECOND time.