The 'update' event fires every time the mouse moves, but the graphics layer won't redraw on the screen, even when cloning the graphic, deleting it from the graphics layer, and re-adding it - the usual fix for a graphic not re-drawing upon being edited.
Oddly, everything works fine if the user zooms in or out of the map while gripping the point. Things start drawing, and the greyOutAllRouteLines function (which sets the colour of every line on the map to grey, to indicate that with the shifted point they're now out of date) works as advertised. In both cases the remove/clone/re-add method is required, otherwise nothing redraws regardless of map interaction.
It feels like the graphics layers are being updated quite happily while the 'update' events are firing, but they aren't being prompted to re-draw until the map is interacted with, at which point they function as expected. Interacting with the map using zoom functions and similar don't trigger the effect.
Here's the event handler: