In a project aimed at measuring the optical Extragalactic Background Light (EBL) we are using the shadow of a dark cloud. We have performed, with the ESO VLT/FORS, spectrophotometry of the surface brightness towards the high-galacticlatitude dark cloud Lynds 1642. A spectrum representing the difference between the opaque core of the cloud and several unobscured positions around the cloud was presented in Paper I (Mattila et al. 2017a). The topic of the present paper is the separation of the scattered starlight from the dark cloud itself which is the only remaining foreground component in this difference. While the scattered starlight spectrum has the characteristic Fraunhofer lines and the discontinuity at 400 nm, typical of integrated light of galaxies, the EBL spectrum is a smooth one without these features. As template for the scattered starlight we make use of the spectra at two semi-transparent positions. The resulting EBL intensity at 400 nm is I EBL = 2.9 ± 1.1 10 −9 erg cm −2 s −1 sr −1Å−1 or 11.6 ± 4.4 nW m −2 sr −1 , which represents a 2.6σ detection; the scaling uncertainty is +20%/-16%. At 520 nm we have set a 2σ upper limit of I EBL 4.5 10 −9 erg cm −2 s −1 sr −1Å−1 or 23.4 nW m −2 sr −1 +20%/-16% . Our EBL value at 400 nm is 2 times as high as the integrated light of galaxies. No known diffuse light sources, such as light from Milky Way halo, intracluster or intra-group stars appear capable of explaining the observed EBL excess over the integrated light of galaxies.