The veracity of stellar evolution models and theoretical internal structure constants may be subjected to stringent tests by using physical parameters obtained from spectroscopic and photometric observations of eclipsing binary systems that exhibit apsidal motion. Two eclipsing binary stars from the southern hemisphere with no prior published spectroscopic analyses were selected for this study: GV Nor and V881 Sco. Spectroscopic observations of these two eccentric binary systems were made at the South African Astronomical Observatory (SAAO) in 2018 and 2019, and their mid-resolution spectra were obtained. The radial velocities were measured using the cross-correlation method as well as by disentangling the spectra. The rotational broadening of the disentangled spectra of the components was also determined. The absolute parameters of these two systems were obtained by analyzing the SAAO-based spectroscopic data in conjunction with photometric data from TESS. Apsidal motion parameters for these two eccentric binary systems were calculated by analyzing eclipse timing variations. Granada and Padova evolution models indicated ages of 340+/-35Myr for GV Nor and 760+/-15Myr for V881 Sco, in agreement with the observational results. The theoretical internal structure constants estimated from the Granada models were compatible with the observational values within the error limits. However, for both systems, it was found that their circularization and synchronization timescales were shorter than their respective evolutionary ages. Therefore, the fact that the components rotate faster than their synchronized values and still have rather large eccentric orbits (e~0.11) challenges present theories of circularization and spin-orbit synchronization.