The phrase ‘puncher’ was an alternative term for a cowboy. It derives from a term of French origin which has been in common use in English for six hundred years, which means to strike or to prod or to poke, including the use of those activities to drive cattle.
The liar and charlatan, Daniel Cassidy, in his atrocious book How The Irish Invented Slang, mysteriously omits these facts from his discussion of the word. He chooses instead to trace the word to the Irish paintéar, which he says means ‘a tying cord or rope, a noose, a lasso, a snare for catching animals …’ He cites Dinneen’s Irish dictionary as a source. Mysteriously, he omits some pretty important information from this dictionary too. Dinneen’s entry for paintéar begins thus: ‘a painter or panter, a snare, noose, gin or trap, a binding cable …’
In other words, this is an Irish word, certainly, but it is an Irish word of English origin. It is derived from the word painter, which is a nautical term for a rope used to tie up a boat. This is also of French origin (i.e. the English borrowed it from French) but unrelated to the French term which is really the origin of puncher.
To drive the point home, you obviously don’t get to be that incompetent by accident. Cassidy deliberately missed out the important information relating to the real origins of puncher and the real origins of paintéar in order to magic a fake connection into existence. What a con-man!