Odd Gonorhynchus and Late Cretaceous Sapperichthys now nest basal to European and garden eels in the LRT, derived from sailfish ancestors according to the LRT

Gonorhynchus, the beaked salmon, is the real problem.
Based on comparative anatomy, the premaxilla is now in five parts. The dentary in two parts for each side of the jaw. How the jaw works is still unknown. Someday a YouTbe

A YouTube video
(below) shows Gonoryhnchus (aka Gonorynchus) swimming with flicks of its tail and the pectoral fins held nearly motionless, as in swordfish and sailfish.

Gonorynchus gonorynchus
(originally Cyprinus gonorynchus Linneaus 1766; 60 cm) has several common names including beaked salmon, ratfish, mousefish, sand eel, sand fish and shark whiting. The circumorbital bones are absent. The jaw elements lack teeth. This nocturnal fish eats zooplankton and buried invertebrates, then buries itself during the day.

Gregory 1933 reported, “It has an elongate cylindrical body and a sturgeon-like head with a pointed snout, a small inferiorly-placed mouth and a rostral barbel. The body and head are covered with small spiny scales.” Here several bones labeled in Gregory 1933 are relabeled according to Pentanogmius and European eel (Anguilla) homologs. A notochord pierces the well-ossified abdominal vertebrae. The torso is squarish in cross-section. The pectoral fins are essentially immobile.

A postorbital is absent. The prefrontal is separated from the postfrontal. The tail is diphycercal. The prefrontal sits atop a segment of the postfrontal.

Sapperichthys chiapanensis
(Amaral et al 2013, Cenomian, Late Cretaceous, 90mya, 15 cm est length) is an early gonorynchid, derived from Late Cretaceous Pentangmius and basal to European eels, Fossil in situ shown actual size.

This appears to be a novel hypothesis of interrelationships.
If not, please provide a citation so I can promote it here.

References
Amaral CRL, Alvarado-Ortega J and Briot PM 2013. Sapperichthys gen. nov., a new gonorynchid from the Cenomanian of Chiapas, Mexico. In: Mesozoic Fishes 5 – Global Diversity and Evolution, Arratia, Schultze and Wilson (eds.): 305–323. by Verlag Dr. Friedrich Pfeil, München, Germany – ISBN 978-3-89937-159-8
Linneaus C von 1766. Systema naturæ per regna tria naturæ, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis. Tomus I. Editio duodecima, reformata. pp. 1–532. Holmiæ. (Salvius)