The molecule 1,3:2,4-di-O-benzylidene sorbitol (DBS) is a common "gelator" that forms thermally reversible gels in diverse organic solvents. Solid-state C-13 and H-1 NMR techniques, along with electron microscopy, are utilized in an exploratory study of DBS in the gelled state where we consider both in situ and dried gels. The gels were formed in either acetone or benzene, with the former being a better solvent for DBS. We find the in situ or dried DBS gels to be composed of rigid twisted nanofibrils (similar to 15 to 21 nm in diameter). The fibrils show local molecular ordering, but not crystalline order, and they contain no trapped solvent. The molecular mobility at the fibril surface is modestly enhanced, and all the free hydroxyl groups of the sorbitol moiety are involved in strong hydrogen bonding. We also attempted to find a truly crystalline form of DBS whose structure, as judged by the similarity of C-13 spectra, is close to that of the fibrils. We partially succeeded in this quest, employing melt crystallization followed by slow cooling. However, this sample was a mixed crystal having small domains, where only one type of domain was structurally similar to the fibrils. We also investigated the long-time evolution of the in situ DBS gel network. Specifically, high-resolution NMR kinetic studies were performed over periods of days where the residual concentration of DBS in acetone solution was monitored during and after gel formation. The DBS concentration on these long timescales evolved slowly, and we introduce a simple mathematical model and equation to describe this phenomenon.