Harrisville?5915 has it, once again.
I would have posted a "give away" clue today if no-one had got close.
I didn't realise that there were that many lines closed in close proximity in 1964 but the "equidistant?" If you drew a line between Allora & Killarney, took the mid point and then drew another line at right angles to that point, one of the directions would have taken you very close to passing through it. (You would do that by observation, of course). The other in the wrong direction.
The Triangle at Harrisville would have given it as a suspect as to the line extension at that point.
Maybe I've just given away 5915's method.
There's an interesting 'photo of Harrisville on this site:-