What is mobile connectivity like in Israel, especially outside the cities but also in the smaller cities? For example, will I be able to use GetTaxi, the Israeli equivalent of Uber, at the Beit She’an / Sheik Hussein – Northern border crossing (between Tiberias and Jerash)? More generally, will there be connectivity in smaller cities, along the major roads between cities, and at tourist attractions?
Israel is a small country that looooves its mobiles. Excluding some bits of the Negev desert, the entire country is blanketed with mobile phone networks, and you're not going to have any trouble anywhere populated.
Here's an unofficial coverage map for Pelephone, one of the big local operators. Note that this is crowdsourced from users, and the actual coverage is considerably better. Also, the Palestinian bits have their own operators, which is why the West Bank and Gaza show up as blank.
The map is in Hebrew, but you can just zoom in on any part to see the cellular coverage.
Sample screenshot from Tel Aviv area: