Trying to understand triangulation

 

I am trying to discover how I am related to person M.  We have no surnames in common but have locations in Cheraws District, South Carolina and Woodville, Mississippi in common. 

I used Gedmatch to find all the kits that match Nikki, person M, and me and then painted chromosome 1 using the new DNA Painter (http://dnapainter.com ) These kits match from 113,140,172 to 159,942,204 or parts thereof.

Each of these people is in common with me and M.  This is the only in-common-with segment and it ranges from 13 to 25 cMgs. All of the data are from GEDMatch.  Part of this area is a common pile-up area, see the gray at the top. 

Using the Triangulation tool at GEdmatch, only B, N, M, and me form a triangulated group. M, I, and C are known cousins but are not in our triangulated group.

Why are there not more people who triangulate? Why would A, C, D, E, F, and G not be part of this group?  What about I, J, K, and L? Would this distribution indicate descent from different couples?

Looks like I have research to do. What steps should I take now?