Finding path between points via non-linear lines

Hello, I'm trying to figure out a way to take two sets of data, one a set of xyz coordinates of "terminals" and the other set points on a 3d line that connect the terminals. I can't figure out how to apply path finding algorithm to this. I was trying to simplify it down to the start points and endpoints of the lines and doing nearest neighbor search but I cannot seem to figure out how to do it. Any advice would be appreciated. Side note the terminals don't exactly exist as points on the lines, but I could solve that just by evaluating the distance from the start/endpoint of a line. Then some of the lines have same endpoints and sometimes branch.

[Image Analyst]

Do you have any kind of data, diagram, figure, picture, plot, or anything at all that would help illustrate your problem? Because I'm not sure what a terminal is. Is it a computer monitor, a bolt on an electronic/electric circuit, some sort of end node on a graph, or something else? Go to snag.gy and paste in a picture to explain your situation. There are lots of pathfinding code in the File Exchange. For example, search for A* (my personal favorite method).