13-Jul-2021 -- I was in Durango, Colorado on vacation for a couple of days, and decided to take a break from mountain biking to visit this Degree Confluence Point, not far to the South. I followed the directions suggested by Shawn Fleming. It was interesting to see the extensive natural gas facilities in what would otherwise be a desolate area. I parked at a turnout at [36.997091,-108.00230] - 0.24 miles from the point - and hiked the rest of the way.
The Degree Confluence Project considers this point to be exactly on the border between Colorado (to the North) and New Mexico (to the South), so - according to its rules for borders - it assigned the point to New Mexico. However, it seems that the point actually lies within Colorado - barely - because there is a fence (running East-West) just 60 feet South of the point. The point lies among stunted, thinly-spaced pine trees (with occasional cactus). In mid-July, the ground was bone dry. This point reminded me a lot of [38,-109] - the point just to the Northwest - that I had (re)visited two months earlier.
Here is a remote-controlled aerial video of this confluence point.