The British-English phrase a racing dog’s bollocks is used in similes to denote something that protrudes.

(Remark: The image of something ‘sticking out like a dog’s ballocks’ might be the origin of the British-English slang phrase the dog’s bollocks, also the bollocks, meaning the very best, the acme of excellence—cf. meaning and possible origin of ‘the (dog’s) bollocks’.)

The phrase a racing dog’s bollocks originated in British military slang. The earliest instance that I have found is from Northern Ireland: Soldiers Talking (Sidgwick & Jackson – London, 1988), by Max Arthur:

“I tell you, I’ve never seen anybody come round a corner so fast: the biggest wolfhound I’ve ever seen was chasing him down the street. He’d barked and this hound had come straight over the fence after him. He was running for his life. All we could do was fall about laughing literally. He had eyes like a racing dog’s bollocks, and he was only a small stocky bloke.”

Rick Jolly defined the phrase in Jackspeak: The Pusser’s Rum Guide to Royal Navy Slanguage (Palamanando Publishing – Torpoint, Cornwall, 1989):

sticks out like — Both Jack and Royal have a number of favourite descriptive comparisons for items such as nipples that are especially prominent:
– a racing dog’s bollocks
– a blind carpenter’s thumbs
– [&c.].

The phrase also occurs in Reflected Glory: A Portrait of Britain’s Professional Elite (Otter Books – Honiton, Devon, 1990), a “picture of life in the Royal Marines”, by Carney Lake:

‘Cocky bastard, eh?’ thought the PJI [= parachute jumping instructor]. A lot of the booties he had had in the past liked to think they were hardmen, supermen, uncrackable, that type of thing. Here apparently was another. Throwing abuse and fishing for bites off the instructors all the first week, that was him. Needed taking down a peg or two. Well, there were two easy ways to do that from a balloon. One was to tell the man to go in his own time. That sorted the wheat from the chaff, that did. They just couldn’t bring themselves to do it. Didn’t have it inside ’em. But for the real hard nuts like this geezer, there was only one way. Which was to give them the ‘Go’ whilst holding onto the back of their ’chute, then pull them back in. It worked a treat. Every one a winner! They got all steamed up, went to jump, stepped off and found themselves back in the cage when they thought they ought to be falling. It was a beaut! It never failed. You should see their faces; panting, snarling, eyes like the proverbial racing dog’s bollocks. It cracked the hardmen right open, that one did. Like throwing a firecracker into a greyhound’s starting cage. A real peach.

The following is from Going Commando (John Blake Publishing Limited – London, 2015), described by its author, Mark Time, as “a personal reflection on my early years as a Royal Marines recruit”:

Since inception it [= the SA80 rifle] has caused controversy, and initially its faults were many. Some of the more typical faults we found within the first two weeks of issue were:
[…]
The magazine release catch: aptly named, every time it would catch on something the magazine would release – usually by accident. It stood out like a racing dog’s bollocks; every time the protrusion was knocked, rubbed or given a stern look, it would cause the magazine to fall out of its housing, usually unbeknown to the operator of the weapon.

The earliest non-military use of the phrase that I have found is from Horse’s Arse (Headline Publishing Group – London, 2010), “a story about a fictional sub-divisional police station, set in a fictional county in the mid 1970s”, by Charlie Owen, who “enjoyed a thirty-year career in the police service”:

Clarke replaced his phone and sat rubbing his throbbing temples for a while. He’d had a skinful the night before; his eyes looked like a racing dog’s bollocks and he was suffering. He’d contemplated going sick but his DCI had been at the same do with him and questions would be asked if he failed to show.