When I did a recce of the area some time back I wish I had filmed the entire route from the murder scene, across the road where the two women in a car saw Mitchell, over the gate, through the wood, across the river, through another wood and up into the housing estate a matter of 30 seconds from his house. I guarantee he could do the entire route in less than 10 minutes no problem.
I may do this at some point in the future. I stay in the North of Scotland, so that's a 3-hour drive to get there under the current covid circumstances, is not possible at the moment.
Here is a screenshot of the signpost on Newbattle Road that informs people that the path is there. If you travelled down Beeches turned right, the signpost is aprox 100 yards farther down the road on the left-hand side (redwoods house side). Roan Dyke path is only another 20 yards or so farther down on the right hand side. The gate(no longer there) where Luke was standing just a wee bit more down the road on the left hand side.
I don't think Luke took this entrance to the path, like has been mentioned, I think he leaped over the gate and into the woodland that way, then towards the river. I would even say, he did not need to use the path, staying in the woodland until he reached the river. I also suspect he knew this little woodland and river very well. It was right on his doorstep.