This question is a request for general explanation of an astronomical phenomenon known as "Pallas libration", and isn't much about the details of Gauss's mathematical model of this libration. As is well known (see this post: Calculation of Gauss leading to 18:7 resonance between orbits of Jupiter and Pallas), Gauss discovered a $18:7$ resonance of Pallas with Jupiter, and according to the source given in https://aas.org/archives/BAAS/v31n5/aas195/431.htm ("On the Commensurate Motion of Pallas") he developed a theory of the periodic libration of Pallas with a period of $737$ Jupiter sidereal periods (Werke v. 7, p. 421, p. 559). Martin Brendel, in his essay on Gauss's astronomical works, also commented about Gauss's theory of libration (he actually devoted an entire section to it in his essay).
The basic point i don't understand is the use of the word "libration" within the context of the motion of asteroids - as far as i know, libration is a phenomenon in which an observer on a planet (Earth, for example) is able to see more then a half of an orbiting moon which is in a "tidal lock" with the planet (the effect in which tidal forces and moments synchronize the rotational angular motion of the moon with his orbital angular motion). This is caused by visual effects such as the parallax derived from the change in positions of the observer. But Pallas isn't even a moon of Jupiter, needless to say in "tidal-lock" with Jupiter. So i'd really like to get an explanation on this.
Although this question is more about the physics involved then about the historical circumstances, I chose to mention Gauss and ask it on HSM stackexchange, simply because he was one of the few astronomers that attempted to formulate such a theory (which is quite a "niche" in astronomical sciences), so one can't really seperate the science from it's history and discoverers in this case.