The preoperculum and the ‘preoperculum’ are not homologous

Added Feb. 23, 2020:
A suggestion for the second ‘preoperculum’ that does not contact the hyomandibular and quadrate: Call it what it is: a post squamosal.

According to Wikipedia,
“The preoperculum is a crescent-shaped structure that has a series of ridges directed posterodorsally to the organisms canal pores. The preoperculum can be located through an exposed condyle that is present immediately under its ventral margin; it also borders the operculum, suboperculum, and interoperculum posteriorly.”

Figure 2. Eusthenopteron skull showing some changes from the Cheirolepis skull.

The wiki-authors are referring to the majority
of preoperculum appearances in vertebrates (Fig.1 ), ignoring the others (Figs. 2-3).

Figure 3. Subset of the LRT focusing on basal vertebrates and highlighting the appearance of the preoperculum in various ways. Note the reappearance of the preoperculum in the tetrapods within the  Ossinodus clade.

A preoperculum can also appear
as a bone posteriorly bordering the squamosal and quadratojugal (Figs. 2-4). Intervening taxa have no preoperculum, so the various appearances of this bones are not homologous, but keep returning as reversals. Note the appearance of a preoperculum in most extant fish and in unrelated catfish, too.

Figure 4. Ossinodus is a close relative of Trimerorhachis in the LRT.

Among tetrapods
the preoperculum makes a brief reappearance in the Ossinodus (Fig. 4) clade.