Conjecture on tangential accumulation of parabolic curves

Let $l$ be a parameter on the unit circle, so that $|l|=1$. A parabolic curve is a parameter curve along which the corresponding maps have a parabolic cycle.

Parabolic-curve accumulation conjecture. Parabolic curves accumulate on the unit circle at isolated points and tangentially to it. Moreover, if a parabolic curve accumulates on a parameter $l$ with $|l|=1$, then another parabolic curve of the same period lands on $l$ from the opposite side.

This conjecture describes the numerically observed accumulation of boundaries of hyperbolic regions, including extended tongues, on the unit circle. The supplied text presents it as a numerical conjecture, with no resolution stated.