We used the ultra-deep GLIMPSE JWST/NIRCam survey to constrain the faint end of the [O  III ]+H β luminosity function (LF) down to 10 ³⁹ erg s ⁻¹ at z  ∼ 7 − 9 behind the lensed Hubble Frontier Field galaxy cluster Abell S1063. We applied a spectral energy distribution fitting on a Lyman-break galaxy selected sample of 164 lensed galaxies and measured their combined H β +[O  III ] λλ 4960, 5008 flux to build the emission line LF. We found a [O  III ]+H β LF with a faint-end slope ( α = −1.78 ^+0.06 _−0.06 for z  = 7 − 8 and α = −1.55 ^+0.11 _−0.11 for z  = 8 − 9), which is flatter than the UV LF at similar redshifts ( α  ≤ −2) and suggests a lower number density of weak [O  III ]+H β emitting galaxies at fixed M _UV . We analysed several possible explanations: (i) a decrease in the [O  III ]+H β -to-UV ratio due to bursty star formation histories (SFHs), (ii) the effect of metallicity on the [O  III ]-to-H β ratio, or (iii) signs of a faint-end turnover in the UV LF. Under the assumption of an evolving [O  III ]-to-H β ratio, we separated the contribution of [O  III ] λ 5008 and H β and obtained a flatter [O  III ] λ 5008 LF ( α = −1.66 ^+0.05 _−0.05 for z  = 7 − 8 and α = −1.45 ^+0.09 _−0.10 for z  = 8 − 9) but steeper H β LF ($ \alpha=-1.95_{-0.08}^{+0.08} $ for z  = 7 − 8 and α = −1.68 ^+0.13 _−0.14 for z  = 8 − 9). The combination of a decreasing metallicity and bursty SFH can reconcile the observed differences between the UV and [O  III ]+H β LF. By converting this LF into the ionising photon-production rate Ṅ _ion , we show that galaxies with L _{H α}  ≥ 10 ³⁹ erg s ⁻¹ , that is, with a star formation rate (SFR) (H α )  ≥  5 × 10 ⁻³ M _⊙ yr ⁻¹ ) cause 31%−90% and 46%−156% of the ionising photon budget (at 7 <  z  < 8 and 8 <  z  < 9), when we assume a constant escape fraction of Lyman-continuum photon ( f _esc  = 0.14). The shape of the LF further shows the negligible contribution of faint galaxies to the Ṅ _ion . Additionally, we derived the cosmic star formation rate density (SFRD), finding results consistent with previous estimates. However, the sensitivity of GLIMPSE to lower SFRs reinforces the conclusion that very faint galaxies contribute very little to Ṅ _ion and the SFRD. Our results suggests that GLIMPSE has detected the bulk of the total [O  III ]+H β emission from star-forming galaxies, and that galaxies below our detection limits are likely minor contributors to cosmic re-ionisation.