It looks like the tracking signal is missing so the vcr isn't locking on to the video on tape at all. That could be caused by a bad cable, dirty connections, very worn, dirty and/or misaligned control/audio head or electronic issues. If the same tape plays totally fine on the S7500 and other VCRs that points to a VCR rather than recording issue (unless it's the very rare case of the original recording and the S7500 having a very similar misalignment or something.) Especially since the S7500 and S7860 as far as I know use very similar mechanisms.
maybe first things I would try is cleaning the audio/control head with q-tip or similar + alcohol, and re-seating the cable that goes to it a few times.
Another thing that could maybe help with diagnosis if that doesn't help is to if audio playback (linear, not hi-fi stereo) sounds different between the decks as that could indicate difference in Audio/control head alignment or wear, and maybe post the clips. Since control track and linear/mono/standard audio goes via the same head and cable bundle so there can often be some overlap between issues. Check with a tape section that isn't dropping out (as that will probably have warbly audio due to the lack of tracking).
I have experienced the occasional loss of tracking on the related Philips VR1100 (which is mostly the same as the JVC HR-S78xx decks.) so maybe it was a similar issue.
My Video gear overview/test/repair/stuff yt channel http://youtu.be/cEyfegqQ9TU