Tax is ‘dachshund’, a Swedish short version of German Dachshund, which has been borrowed whole into English. Literally it means ‘badger dog’, Dachs is ‘badger’. Perhaps the badgers got that name because of their skill in making their setts: Dachs comes from Germanic *þaksu-, ‘builder’ from the Indoeuropean root *tecs ‘shape, ‘build’. Relatives are Greek techno- ‘art’,’skill’,’ craft’, ‘method’, ‘system’ and probably Latin texere ‘to weave’. Also Swedish täxla ‘small axe’.
The origin of English badger is unclear, perhaps it is called so because of its ‘badge’, the white blaze on the forhead.
Swedish grävling is simpler: from Low German grevel, Germanic grabila- combined with Danish græving, of course from a Germanic root *grab ‘to dig’ from Indoeuropean *ghrebh- ‘to dig’, ‘to scratch’, ‘to scrape’.
When I checked about the dachshund a word came up in my mind that I haven’t heard since childhood: Dachsbracken. Now I know from Wikipedia: “The Westphalian Dachsbracke is a small, short legged scenthound, a breed of dog originating in Westphalia, a region of Germany. The Westphalian Dachsbracke was used in Sweden to develop the Drever.”
In Wikipedia the word Bracke is explained as something to do with brackish water and coastal marches, but that does not sound reliable. Much more credible is the English Online Etymology Dictionary where there is an archaic English word, brach, ‘bitch hound’, originally 'hound that hunts by scent', from Old French. brache, brachet, of West Germanic origin, and also an Old High German word braccho ‘hound’, ‘setter’, from Indoeuropean *bhrag- ‘to smell’ from which comes Latin fragrare.
This little fellow was dancing around, euphoric about his booty.