27-Dec-2001 -- A couple of days after Christmas my brother-in-law and I decided to give 34°N 104°W a try and this confluence lies essentially on the way.
We headed east on I-40 from Albuquerque and exited the freeway at the Montoya exit. There we took county road BK south and soon encountered a locked gate with a nasty 'Road closed' sign. We were still 4.5 miles from the confluence. We turned around and stopped at a little ranch where we were immediately greeted by a number of friendly dogs. I went up to the house and the lady of the house came out to meet us. We explained our mission and asked for permission to use the dirt roads on the ranch land. The lady explained to us that she and her husband don't own the ranch and that she could not give us permission. Her husband would not be back till late in the afternoon, he would be able to decide. We asked whether we could call somebody (husband/owner), but she was obviously not comfortable with giving a phone number to strangers. She asked why we couldn't just take pictures from right where we were.... Not getting anywhere we thanked her and left.
It is not clear that the confluence actually is located on the ranch we visited, but there is a very high probability that the confluence is located on somebody's ranch and/or that private land has to be crossed to reach it. On our way south we tried some roads off of Hwy 209 and they all got us to 'No Trespassing' signs.
The best approach to visit this confluence might be to get hold of some landownership information and contact all the owners whose land has to be crossed in order to get to the confluence.