How to Micro Manage Manipulator When in Edit Mode, I find sometimes I want to move an edge, or at least two vertices, in a direction that would be perpendicular to their orientation along their existing edge.

At that moment, the Transformation Orientation selections (Normal, Local, Global, et al) have no vectors pointing in that direction.

How might I, or is it possible to, change the "polarity" of those manipulator vectors (independent of the given selections: Global, Local, Normal, Gimble, View) so that one of them is pointing in the perpendicular direction to the line/edge between the vertices?
Enter Edit Mode, switch to Edge selection mode, select any edge, go to the Transform Orientations panel and press the + button to add a new transform orientation while that edge is selected.

You can name your new transform orientation whatever you want, and then use it afterwards. There will additionally be created a new transform orientation named "Edge" that will hold the orientation you want.

You can then move along that edge direction, or perpendicularly to it, relative to the surrounding faces normals.