We present a new method to study the contribution of faint sources to the UV background using the 1D correlation of metal absorbers with the intergalactic medium (IGM) transmission in a Quasi Stellar Object (QSO) sightline. We take advantage of a sample of $25$ high signal-to-noise ratio QSO spectra to retrieve $150$ triply-ionised carbon (cfour) absorbers at $4.5lesssim zlesssim 6.2$, of which $37$ systems whose expected H{~small I} absorption lie in the Lyman-$alpha$ forest. We derive improved constraints on the cosmic density of cfour ,at $4.3< z < 6.2$ and infer from abundance-matching that cfour ,absorbers trace $M_{text{UV}}lesssim -16$ galaxies. Correlation with the Lyman-$alpha$ forest of the QSOs indicates that these objects are surrounded by a highly opaque region at $rlesssim 5 $ cMpc/h followed by an excess of transmission at $rgtrsim 10$ cMpc/h detected at $2.7sigma$. This is in contrast to equivalent measurements at lower redshifts where only the opaque trough is detected. We interpret this excess as a statistical enhancement of the local photoionisation rate due to clustered faint galaxies around the cfour ,absorbers. Using the analytical framework described in Paper I of this series, we derive a constraint on the average product of the escape fraction and the Lyman continuum photon production efficiency of the galaxy population clustered around the cfour ,absorbers, $log langle f_{text{esc}}xi_{text{ion}}rangle /[{rm erg^{-1}~Hz}] = 25.01^{+0.30}_{-0.19}$. This implies that faint galaxies beyond the reach of current facilities may have harder radiation fields and/or larger escape fractions than currently detected objects at the end of the reionisation epoch.
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