Gogonasus also gives us
the origin of the preopercular arising from an anterior/posterior split of the squamosal (Fig. 1). This type of preopercular shrinks and disappears in Late Carboniferous tetrapods.
the preopercular appears in Trachinocephalus (Fig. 2) and in no other taxa derived from that clade. Since this is an extant taxon with a convergent loss of cheek/facial bones it would be good to find out what happened in fossil ancestors here.
By a third convergence
the preopercular has yet another genesis in Pholidophorus (Fig. 3), a trait that continues in all descendant taxa among the remaining ray-fin fish. Is this the same preopercular as in Trachinocephalus? At this point, no. However just a few fossil added intervening taxa would solve this issue.
in Lepisosteus (Fig. 4) the preopercular (light green) has evolved to be like those in pipefish and sea horses: completely horizontal, ventral to the jugal, with the anterior end following the jaw joint (quadrate) as it migrates anterior to the orbit.
also develop a preopercular (Fig. 5).
traits can converge. The same new bone can appear more than once. Or disappear more than once.