How does this strategy for chasing the sunset work?
I would go to the Arctic circle, where you can experience an almost perpetual sunset, without having to drive around.

Edited to answer the question: My interpretation of the diagram, is:


The terminator at a certain time near sunset, is the one shown towards the east (darkness approaches), running NE/SW.
As time progresses, it moves into the top horizontal location, running E/W; this consistent with the more northerly latitudes having continual daytime, coinciding with a certain parallel polar circle.
As morning approaches, the terminator moves towards the west (bringing daylight with it), and runs NW/SE.


I think the arrows would be better if the tip of the one on the right, joined the base of the one on the left, showing your car journey as a continuous one.