We investigate a new class of galactic halo axion detection techniques based on precision frequency and phase metrology. Employing equations of axion electrodynamics, it is demonstrated how a dual mode cavity exhibits linear mode-mode coupling mediated by the axion upconversion and axion downconversion processes. The approach demonstrates phase sensitivity with an ability to detect axion phase with respect to externally pumped signals. Axion signal to phase spectral density conversion is calculated for open and closed loop detection schemes. The fundamental limits of the proposed approach come from the precision of frequency and environment control electronics, rather than fundamental thermal fluctuations allowing for table-top experiments approaching state-of-the-art cryogenic axion searches in sensitivity. Practical realisations are considered, including a TE-TM mode pair in a cylindrical cavity resonator and two orthogonally polarised modes in a Fabry–Pérot cavity.