hi les, ok, if outside sounder is activating then tamper fault is in that circuit. possibly a wiring fault, but if you immediately reset the system and the tamper light goes out then the fault is no longer present.
i would suggest that the cover on the external sounder, which will have some kind of tamper or properly called an anti tamper device. Either a small spring under compression or more likely a micro switch with a long metal lever attached is opening, activating the alarm. the lever will be bent to face the wall and when the cover is in place the switch is pressed closed. same applies to a spring device. you should be able to hear the clicking of either switch as you replace the cover.
have had many experiences of the spring, especially the lever type, flattening out after a long period of time, and when sunlight (or even cold) hits the cover there is enough movement to momentarily open the switch and cause a problem.
I would check this first before looking for any wiring problems although you may find the internal components of the sounder are showing signs of corrosion which might also explain the problem.
alan, May 2020