Context. The study of resonant oscillation modes in low-mass red giant branch stars enables us to infer their ages with exceptional (∼10%) precision. This unlocks the possibility to reconstruct the temporal evolution of the Milky Way at early cosmic times. Ensuring the accuracy of such a precise age scale is a fundamental but difficult challenge. Because the age of red giant branch stars primarily hinges on their mass, an independent mass determination for an oscillating red giant star provides the means for this assessment. Aims. We analysed the old eclipsing binary KIC 10001167, which hosts an oscillating red giant branch star and is a member of the thick disk of the Milky Way. Of the known red giants in eclipsing binaries, this is the only member of the thick disk whose asteroseismic signal is of a high enough quality to test the seismic mass inference at the 2% level. Methods. We measured the binary orbit and obtain fundamental stellar parameters through a combined analysis of light-curve eclipses and radial velocities, and we performed a detailed asteroseismic, photospheric, and Galactic kinematic characterisation of the red giant and the binary system. Results. We show that the dynamically determined mass 0.9337 ± 0.0077 M⊙ (0.8%) of this 10 Gyr old star agrees within 1.4% with the mass inferred from a detailed modelling of individual pulsation mode frequencies (1.6%). This is now the only thick-disk stellar system that hosts a red giant for which the mass has been determined asteroseismically with a precision better than 2% and through a model-independent method at a precision of 1%. We hereby affirm the potential of asteroseismology to define an accurate age scale for ancient stars to trace the Milky Way assembly history.