The alarm goes off after its set is common symptoms of a faulty siren.
Alarm siren, if it’s the original factory fitted unit, is 10 years old, the usually give trouble at 10 years of age. Some are troublesome at 7 or 8 years, others can last up to maybe 14 years before becoming a problem.
You could remove the siren and cut or prise it open and see what shape it is inside.
It could be something else alright but how much will it cost to have someone investigate the fault is outweighed by the cost of replacing the siren.
Dec
Edit;
Below is what happens, over time, to the batteries inside the siren, note the Black damage to the Green PCB.