If it's the same as in my car (Becker box, last digits in part number = 26), then there are a few things that could be wrong.

There are 4 relays in there. 3 for flashing the lights, horn, etc... and 1 that determines if the system is armed or not.

If you have electronics skills, start by checking the little 100uf@10v electrolytic capacitor. If this is shorted, it will cause a current drain.

The ticking sound is probably one of the relays cycling on and off. It wouldn't be the arm/disarm relay as that one is nearly silent.

Does the ticking occur at roughly the same rate as the alarm would beep or the lights would flash? If so, then the alarm is constantly going off, and for some reason not actually honking or flashing.

After doing some basic troubleshooting of all the sensor wiring, etc. I would just try to find another alarm box on Ebay. They're usually $40 or less for a used one. Just be aware, these things do tend to develop issues over time.

I could print out the alarm troubleshooting flowchart for you if you want.

-tp