Horse's Neck

The briefest of searches on Google suggests that the horse's neck can be made with either brandy or whisky and does not include any lime, but the essential twist (pun intended) is a long spiral of lemon peel draped over the edge of the glass.

Taking the first few hits in order:

Wikipedia says it's brandy (or sometimes bourbon) and ginger ale, and not lime but "a long spiral of lemon peel (zest) draped over the edge of an 'old-fashioned' or highball glass."

www.liquor.com says it's bourbon, brandy or American rye whiskey, along with ginger ale and lemon peel. (Note: when I visited this page, it asked for my email address and confirmation that I was over 21. Needless to say, although I might have been prepared to give the latter, I was not going to give the former; interestingly however, after I'd given my date of birth to EJ Brandy (see below), it was happy to show me its recipe.)

Jamie Oliver: whisky, lemon peel, Angostura bitters, ginger ale.

The Spruce: lemon (long peel spiral), bourbon, ginger ale, Angostura bitters. Note that "It's all about the lemon peel" - the ingredient that the MQL question left out.

The vetters did point out Wikipedia's description to the setters, who chose to ignore the discrepancy.

So what is brandy and ginger ale with a twist of lime?

Group Recipes has a cocktail of brandy and ginger beer with lime juice and lime slices, but doesn't give it a name.

EJ Brandy has a cocktail of EJ brandy and ginger ale with a twist of lime peel, but simply calls it 'EJ and ginger'. (Note: this site will ask for your date of birth, but not your email address.)

The best steer I could find on this, however, was from Kitchen Cocktails, which has a recipe for a brandy mule: "Brandy, ginger beer, and a little bit of lime (a riff on the Moscow Mule, which uses vodka instead of brandy). This drink is sometimes known as a Brandy Buck, French Mule, or Horse's Neck."

Kitchen Cocktails is the only one of the sites I've mentioned that thinks a cocktail of the kind described in the MQL question can be called a horse's neck; and it's not even its main name, but just one of three "alternative" names.

Kitchen Cocktails also enlightens us on the difference between ginger ale and ginger beer: "Basically, ginger beer is a way more intense version of ginger ale: while ginger ale is just sugary soda water with a mild ginger flavouring, ginger beer is a spicy, fiery, bold tasting beverage, with little–to–no sweetness, that much closer resembles actual ginger."