By the short hairs
To be 'caught/got/held by the short hairs', or in the UK equivalent, '... by the short and curlies' is to be trapped by an opponent, in a position one can't easily escape from.
Few people would doubt that the short hairs/short and curlies are the pubic hairs and that this phrase is of vulgar origin. Such an assumption would be incorrect. The short hairs in question are the hairs of the neck.
The 'by the short hairs' expression may well have been military and the first example of it that I have found is from The Drums of the Fore and Aft, one of Rudyard Kipling's Indian Tales, 1890, which portrays the British Army's occupation of India:
"They'll shout and carry on like this for five minutes. Then they'll rush in, and then we've got 'em by the short hairs!"
Prior to this, in the same story, a soldier makes an explicit reference to short hairs, which clearly locates them north of the equator:
"Up my back, an' in my boots, an' in the short hair av the neck - that's where I kape my eyes whim I'm on duty an' the reg'lar wans are fixed."
That meaning of 'short hairs' lasted until at least the 1930s, when Dorothy L. Sayers used the phrase in several of her novels. In her 1930 novel Doctors in Case, which she wrote in collaboration with Robert Eustace, we find the line:
"She's evidently got her husband by the short hairs."
It's hard to believe that the creator of the debonair nobleman Lord Peter Wimsey, who, when not writing novels was also a noted theologian, would be referring there to pubic hairs.
The 'short and curlies' variant is where we enter the vulgar barrack room and venture below the waist. This originated as military slang and is first recorded in Eric Partridge's A dictionary of forces' slang 1939–45, published 1948:
"Short and curlies, the short hairs, in the phrase 'He got me by the short and curlies' - he caught me out properly."
Whether this was coined under the false belief that the earlier version referred to pubic hair or whether it was knowingly smutty, it is difficult to be sure. My money is on the latter.