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We present a new method to study the contribution of faint sources to the UVbackground using the 1D correlation of metal absorbers with the intergalacticmedium (IGM) transmission in a Quasi Stellar Object (QSO) sightline. We takeadvantage of a sample of $25$ high signal-to-noise ratio QSO spectra toretrieve $150$ triply-ionised carbon (\cfour) absorbers at $4.5\lesssimz\lesssim 6.2$, of which $37$ systems whose expected H{~\small I} absorptionlie in the Lyman-$\alpha$ forest. We derive improved constraints on the cosmicdensity of \cfour \,at $4.3< z < 6.2$ and infer from abundance-matching that\cfour \,absorbers trace $M_{\text{UV}}\lesssim -16$ galaxies. Correlation withthe Lyman-$\alpha$ forest of the QSOs indicates that these objects aresurrounded by a highly opaque region at $r\lesssim 5 $ cMpc/h followed by anexcess of transmission at $r\gtrsim 10$ cMpc/h detected at $2.7\sigma$. This isin contrast to equivalent measurements at lower redshifts where only the opaquetrough is detected. We interpret this excess as a statistical enhancement ofthe local photoionisation rate due to clustered faint galaxies around the\cfour \,absorbers. Using the analytical framework described in Paper I of thisseries, we derive a constraint on the average product of the escape fractionand the Lyman continuum photon production efficiency of the galaxy populationclustered around the \cfour \,absorbers, $\log \langlef_{\text{esc}}\xi_{\text{ion}}\rangle /[{\rm erg^{-1}~Hz}] =25.01^{+0.30}_{-0.19}$. This implies that faint galaxies beyond the reach ofcurrent facilities may have harder radiation fields and/or larger escapefractions than currently detected objects at the end of the reionisation epoch.

The role of galaxies and AGN in reionizing the IGM - II: metal-tracing the faint sources of reionization at $5\lesssim z\lesssim6$