life being what it is, it will be the siren box.
Lift it off the wall and bring it into the house to test. It will be much easier.
the tamper detector is a sprung plastic lever. It has to press against a firm flat spot on the wall, and the lid pushes on it. If your wall is uneven it may not be pressing hard enough. If you put it on a table or other flat surface in the house with the lid on, it should be pressed. You will see the switch it operates, and it is possible to hold it closed with a rubber band while you are testing.
When you refit it, put it where you can reach more easily. Perhaps you could put it close to an upstairs window that you can lean out of.
If, before that, you want to verify that it is not one of your sensors, take the batteries out of one or more of them for a day and see if the alarms stop. I would suspect a door sensor first, for example if you have a door that rattles in the wind.
During testing, it is possible to set the siren to sound for only one second. That will annoy the neighbours less.
If you have a defective sensor, or siren, you might be able to get one on ebay at modest cost. The sensors from the 6000 range will work with the 3000 range siren (and vice versa) but the keypad is quite difficult to program to match with the other version of siren because the commands are different. An HSA6400 at Ironmongerydirect, is a similar budget DIY wireless alarm, but better.
If the siren keeps going off even after you have taken the batteries out of all your sensors, it might be due to radio interference, which is very rare if you live in an ordinary domestic house. Ensure the siren is well away from your wireless router, baby alarms, wireless doorbells, arc welders and radio transmitters. Occasionally they block signals from sensors, I have never actually known one set off the siren but no doubt it is possible.
You will also get comments from people who disapprove of budget wireless DIY alarms, which will not help with your problem.