Learn English – connection between shy (adj.) and shy (v.) meaning throw

No, aside from the similarities in spelling, there there is no connection between machination and Machiavelli. Machination comes from the Latin root machinat-, which in turn came from the Greek mekhos: "contrivance". There is no convincing evidence to suggest that the name Machiavelli was derived from the word, or any of its roots or later derivatives.

Figurative Meaning

According to the website Words and Phrases from the Past the expression means

• a valuable hint (to tell or give information)

It matches the third example

Look here, you naturalist, and I'll put a wrinkle on your horn [I'll give you a hint]. Yonder hangs a magnificent bunch of fruit that I very much desire to possess

A second variation I found was "Well, that's a new wrinkle in my horn"

We love to get comments about the column. If the readers have heard the expressions that we share they tell us so. But if they haven't, we are sometimes answered with, "Well, that's a new wrinkle in my horn."

• Which is self-explanatory, a sort of I learnt something new today, something else to add to my collection, a novel thought. This fits quite well with the second quote

Let some respectable citizens, gen'lemen, come and take my last dying confession. It'll put a wrinkle or two in their horns, I'll warrant them !

i.e It will surprise/shock them = something new.

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Online Etymology Dictionary reports,

wrinkle (n.)[...]that of "idea, device, notion" (especially a new one) is from 1817.

Why Wrinkles?

From a book entitled Ellis's Husbandry: Abridged and Methodized (1772) there is the following excerpt which confirms @josh61 answer that farmers read the wrinkles on cow horns in order to guess their age, just as many do with the rings on a tree trunk.

This is a surer sign than the wrinkles in a cow's horn, by which we guess at their age; because they seldom have more than one wrinkle or circle, till five years old, and that sooner or later, according to the time of her calving; but an oak, ash, fir, hazel, and most other woods, shew these marks at three or four years old, when they are about the bigness of one's thumb

Here is an excerpt from the Australian Enquiry Book (1897) by Mrs Lance Rawson

To tell the Age of a Cow
At two years of age you will find a wrinkle at the base of the cow's horns, but it is >not fully developed till she turns three. When five years old another wrinkle will form, and after five she will get a new one each year of her life.

Every time you learn something new your brain wrinkles

There is the myth that the brain forms new wrinkles every time new information is stored. Many believe that the more wrinkles the human brain has, the more intelligent that person is. It's only recently that science has proven false that conviction, but it is one that still persists even today, like a popular old wive's tale.

Q. What do brain wrinkles have to do with how smart you are?

A. A lot of wrinkles seems to have more to do with what makes humans smarter than lower animals than with what might have made Einstein smarter than you. [...] Human intelligence appears to be related to the branching of brain cells and the formation of complex links between them, not the shape of the platform where the links take place.

I manage to unearth a very early reference that confirmed people believed every new wrinkle represented a new understanding; this folklore predates Etymonline's estimation by a sizeable ninety-three years, and is found in Jonathan Swift's tale The Wonderful Wonder of Wonders, written in 1720

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Earlier Example of the Idiom

The earliest written example that combined the words new, wrinkle, and horn is in The Medico-chirurgical Review, 1830, New York

Note the variation, to add a wrinkle to the horn (of knowledge)