Painful but safe
That clicking you hear is the sound of energy being discharged along the fence wire, and it’s a safety feature.
The flow of electricity is regulated by the energizer (also called a charger). It stores electrons in a “capacitor” and then releases them in a “pulse”; after each pulse the capacitor stores up electrons for the next pulse.
Clicking indicates pulses being released by the second. However, each pulse lasts a tiny fraction of a second.
Pulsing allows a bear to break contact from the fence once it has taken a shock i.e the connection will last but for a split second so the bear’s muscles won’t lock up and make him “stick” to the fence for a continuous shock. The bear will be able to run away, shaken and deterred, not harmed.
This is a good design feature for you too in case you touch a hot wire by accident (or metal while you’re using the voltage tester)!