I'd rather not reuse tape ... I have tried it, sometimes there's residue from the sticky side if you don't wrap it exactly as before (not a problem if no sticky stuff), and it just didn't looks as nice.
Speaking of Brooks, I love this Cambium Rubber tape ... it seems to be lasting quite nicely, though honestly I haven't had it long -- it's really nice and kind of plushy.
I bought the normal Cambium tape by mistake because the picture the seller used looked very similar, but it wasn't rubbery, so I returned it.
https://www.amazon.com/Brooks-Englan...rubber+cambium