I disagree with the above, here's why:
I know this is an old thread, but I wanted to put up my thoughts and see what people think because I came here when looking for rules clarification.
In my interpretation you can't split up movement between the attacks taken using Two Weapon Fighting action, actually specifically referencing the above rules snippets is where I'm taking my interpretation from. I feel like I'm going a bit mad because I seem to be the only person I can find who interprets it this way, and ordinarily I'd concede that I was wrong due to a much, much greater collective wisdom, but I wanted to throw this out there and see what people thought.
So as the above states (and I think this is actually the best evidence you can't move between the attacks granted by TWF):
"If you take an action that includes more than one weapon attack...".
Now with TWF you are not taking an action that includes more than one weapon attack, as it does with the extra attack feature, you are using a bonus action that is triggered upon making a melee weapon attack to then make a further attack. It is not part of the same, single attack action (as with the 'extra attack' ability, where making an attack action results in being able to make two, separate weapon attacks).
I would also consider the trigger of when it's possible to take the bonus action as "...when you make a melee attack" meaning at the time of taking that action. This bonus action could be triggered on any melee attack (considering action surges or extra attack) but only once per turn and only at the time of making a melee attack.
I feel like it doesn't make mechanical sense considering the rules quoted above, also considering that playing it this way is basically giving any character the 'extra attack' feature, which as I understand it, is supposed to be a fairly good step up in terms of player power when they reach 5th level. I might be wrong but at least using DnD beyond quite a few of the 'physical' classes came with the two weapon fighting action, I doubt that wizards and sorcerers get it.
I also feel that thematically it doesn't make sense. What we're talking about here is someone hitting someone with the sword in their right hand, then running and hitting someone else with the sword in their left hand. I mean they don't need to be using two weapons at this point. As opposed to making both of the attacks together at the same time, which would then look and feel more like two weapon fighting because you're using the weapons at the same time.
Pretty sizable post, wanted to get all my thoughts down. If anyone does want to comment and shoot this down, please specifically include which parts of the rulebooks or whatever that you're using that makes you believe it acts this way. If it is the above snippets from the previous posters then I guess we just have a different way of looking at those and I'm probably wrong considering that everyone else is on your side :)