To use the GreenSquares gadget to flip the starting points on every other vector, add a line that is below the (Assuming vertical) vectors, at a distance about equal to the length of the lines, and select it and every other line and then run the gadget. The extra line is to to provide an offset to the center of the GreenSquares selection bounding box.
I would move the selected vectors to another layer and turn off the original layer for convenience in working with them, but this is not necessary .
If you select all of the vectors and open the Offset tool, you can see where the start nodes are on all of them.
Good judgement comes from experience.
Experience comes from bad judgement.