Ten years ago the Parents Circle - Families Forum set up a free telephone service to enable Israelis, Palestinians and US citizens to "Call over the Wall" at no cost.
Could that scheme be adapted to the internet? This would cost very little to run. Anyone willing to listen, one-to-one, across the Wall, could be asked to complete a confidential profile form enabling the coordinator to act as a sort of "dating agency" linking a nurse to a nurse, a farmer to a farmer, a granny to a granny, a cyclist to a cyclist, a footballer to a footballer, and so forth. Language difficulties may call for patience with internet translation services.
Some Palestinians would object to this as "normalisation", so the arrangement may have to be three-way at first, with a Palestinian and an Israeli both linked to the same European.