The dog, tool(s), and worker all mean "digger." From the Middle French terre. Finisterre is land's end; terrier a burrow and tarriere an auger style "post hole" digger.

TARIERE, Fr. Auger, wimble, gimlet. The French make a diftinction with refpect to the gender of this word. When they exprefs a large fized auger or wimble, they fay, Un gros Tariere, making it mafculine, and when they mean a fmall fized one, they fay, Une petite tariere, making it feminine.

TARIERRE, Fr. likewife fignifies a miner's tool with which he bores into the earth. It is ufed to force a lighted match into the chamber of a countermine, and to make it explode.

A New and Enlarged Military Dictionary, also the French Phrases and Words, London, 1802

And the digger that has to stay behind to light the fuse, is tarrying too.