I had the jog/shuttle cable break on my HR-S8600EU (which the PAL equivialent of the US HR-S7600U I think). I got a replacement from this
thisaliexpress store (plus some others to fix my HR-SS6900), similar to what others have suggested. The connectors on the cable have a 1.25mm pitch which seems to be what most flat flex cables you find in vcrs (other than late combos maybe) were. I generally prefer to buy electronics stuff from digikey, mouser and the like but they don't seem to have much variation of options for pin count and length for 1.25mm pitch flex cables so ended up getting from alix instead. they seem to work fine so far. (Though measure to make sure you got the right pitch, I managed to order the wrong one at first.)
Alternatively it's possible you can salvage one from a different type vcr - most from the mid/late 90s and on use one at least for the A/C head, though those are often 7 rather than 6 pins and may not be long enough.
The cable being absent in my S8600 didn't cause it to not work though (other than the jog/shuttle not working ofc) so maybe there is something more going on.