The insulator is what you guessed. It's the small rubber sleeve that you used to keep your positive and negative leads from touching when you rebuilt the head. You can buy NR wire, I use silver wire. You would just attach a small lead of it to the positive and negative ends.
You may find it more trouble than it is worth. I no longer use vivi novas, and the inconsistent burnt taste is one of the reasons why.
If you're already starting to rebuild coils, I would keep browsing this sub forum if I were you. RBA are now exploding in the marketplace. A year ago they were fairly expensive if you wanted a decent one. Now there are many solid, serviceable ones for sale at really decent prices.
As others have pointed out, if you are set on the vivi nova, there are many YouTube rebuild videos you could browse. I'm sure some of them deal with nr legs.
Cheers.