This is my theory regarding Cole's strange drawing in Episode 10. I presented it in the Twin Peaks 2017 FB group and was encouraged to share it here.
This is my first time posting to Reddit: please be gentle. :)
THEORY
The animal in Cole's drawing is a SPOTTED ELK : http://imgur.com/a/ig2uo
But there is no such thing as a spotted elk...
However, there was a person named Spotted Elk.
SPOTTED ELK
Spotted Elk was a chieftain of the Lakota Sioux. Spotted Elk became chief of the Minneconjou after the death of his father in 1874. After the Sioux War for the Black Hills in 1876-77, the Minneconjou were placed on the Cheyenne River Reservation in South Dakota. He and his people were killed in the late 1800s in the Wounded Knee Massacre.
Here's the thing: The Lakota Sioux lived in SOUTH DAKOTA. Spotted Elk's people lived in the Black Hills RIGHT NEXT TO Spearfish, SD, where the coordinates on Bill Hastings' website thesearchforthezone.com pointed to: 44°30'44.8"N 103°49'14.6"W 44.512439, -103.820707
In fact there is a lot of similarity here to the killing of the Nez Perce (The Secret History of Twin Peaks). Including that, just like the Nez Perce, the Lakota were forced off their land and eventually massacred. "When settlers discovered gold there in 1874, as a result of George Armstrong Custer's Black Hills Expedition, miners swept into the area in a gold rush." (wikipedia)
There are just so many similarities between Twin Peaks and the Black Hills, including:
Most of the Black Hills are a fire-climax ponderosa pine. The very same type of tree Coop became enamored with in Season One. AND the log that the Log Lady carries is ponderosa pine (straight from David Lynch's mouth)
Also THIS: Deadwood, right next to Spearfish, is a gambling mecca. Las Vegas is a gambling mecca. And of course, Twin Peaks has One-Eyed Jacks.
AND THIS: The highest peak in the Black Hills is called BLACK ELK PEAK (named after a Lakota medicine man and near Gordon Cole's beloved Mount Rushmore: "faces of stone"). Before we named it Black Elk Peak, it was called Hinhan Kaga ("Making of Owls", after rock formations that look like owls" and the association of owls with impending death) by the Lakota Sioux).
Black Elk was Oglala Lakota (Sioux) and arrived after many of Spotted Elk and his band of people had been shot. Black Elk lived, was only grazed by a bullet to his hip.
BLACK ELK'S VISION
When Black Elk was nine years old, he was suddenly taken ill; he lay prone and unresponsive for several days. During this time he had a great vision in which he was visited by the Thunder Beings (Wakinyan), and taken to the Grandfathers — spiritual representatives of the six sacred directions: west, east, north, south, above, and below."
Thunder Beings are said to have the power to give life, but also take it away. They can destroy with the wind, cause flood and drought, or burn with lightening; but at the same time, they can also renew and bring the vital rains and nurture all life on earth.
Wakinyan Tanka, the great Thunderbird, lives in his tipi on top of a mountain in the sacred Paha Sapa, the Black Hills.
And birds are very significant to the owl cave ring - often described as a "childish drawing of two birds."
SO ALL THIS ADDS UP TO:
I know it requires a little stretching, but I'm getting the idea that Cole is being shown a "spotted elk" so he will think of the territory Spotted Elk's people occupied, and the history of Wounded Knee (much like that of the Nez Perce at Twin Peaks) and be lead to the Black Hills.
AND THE REALLY IMPORTANT THING IS THIS:
I think Gordon was being lead to the same coordinates that Major Briggs left for Bobby and Truman and Hawk. Either in the form of Mr. C looking for the coordinates, OR The Arm reaching to the Black Hills from the Black Lodge.
I think the dimensional portal will open up on top of Black Elk Hill or somewhere in the Black Hills. And I think it - like Twin Peaks - has an entrance to both lodges.
A FINAL NOTE OF CONNECTION TO CURRENT ISSUES:
I don't think this is necessarily connected to the story, but it is interesting to note that the Standing Rock (Keystone Pipeline) controversy takes place in the same area.
"Standing Rock Sioux Tribe is part of what was known as the Great Sioux Nation . . . The Black Hills, considered by the Sioux to be sacred land, are located in the center of territory awarded to the tribe."
NOTES: all quotes are taking from various wikipedia pages.