Non-extendability conjecture for signotopes of even rank

Let an $r$-signotope be a signotope of rank $r$, and call it 2-extendable if every pair of prescribed crossing points can be contained in an extending element of an extension to an $r$-signotope on one additional element. Even-rank non-extendability conjecture. For every even rank $r\geq 4$, there is an $r$-signotope which is not $2$-extendable. The theorem proving 2-extendability for every odd rank leaves the even-rank case open; examples are known in ranks $4,6,8,10,12$.