First, remember that a Deputy was a highly trained, and experienced man.
Tapping walls or roofs to check firmness will give distinctive sounds if loose rock is present, a metal or wood tool can be used as the difference in sound is still clear.
Also the deputies stick can be used to check the tightness (safety) of wooden pit props. Again the sound is very different between loose and tight timbers.
In many circumstances, you want to give walls, or timberwork a gentle tap, not a good thrashing which could bring it all down on top of you!