There is a large capacitor in the siren that will run for about 20-30 minutes depending on its age. And the bad part is that it only takes about 30 seconds to fully recharge.
Thankfully mine has kinda packed it in and will sream for about 30 seconds before it runs out of juice.
About 4-5 inches from the siren (heading towards to the headlight) there is a connector under all of the electrical tape that I guessing is there. If you disconnect that and let the siren drain the capacitor on its own then you shouldn't have any problems in the future. Throw some blankets or towels on the siren, close the hood and grab a beer or two while you wait for the siren to run flat.
My ultimate goal would be to have a second connector sticking out of the electical tape that I could plug a small 12v battery to while I disconnect my car battery.