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Julesa, by the looks of it, it's more probable that the alarm is activating the lights. You might not have noticed this because it's possible there is no siren connected.
Since you've already told me that your battery has died, I'll have to assume that disconnecting the battery won't help reset the fault. the best thing to do is find someone---or buy a cheap one at a parts/tool store---with a stethoscope. This will help you locate the relay (probably for the alarm).
Once you unplug it see if the lights go out for good. If they do, you'll have to test the hot wire going IN to the relay to make sure it doesn't shudder juice to the relay. This is done with a test light. If the hot wire is constant, than your problem lies with the relay, of which should contain a part number on its housing. If power wire does sputter (on and off) juice, than you have an electrical problem beyond the capabilities of home repair.
Just an amend um here. If you cant get your hands on the test equipment right away, you might try another approach. while you're hearing the clicking relay, start removing the fuses one at a time from the fuse box. if the clicking stops and you've found the fuse that feeds it, you can reference the number fuse to the owners manual (usually tells you what that fuse feeds) and you have it narrowed down to one or two circuits. Good luck!!!