Neither, because it would require a compromise from both side and by definition that means losing since you don't get what youy want and so far the reason they are in this conflict in the first place is because neither wants to lose.
What compromise would it take on Israel's side? What does Israel want to do that involves crossing the Gaza border? I cannot think of anything Israel might possible want to do that would involve crossing the Gaza border. From my point of view, if that border was perfectly sealed and nothing (no rockets or anything) could get through, I would be perfectly happy with the situation. (And you might think that it would be nice if people could still pass through the border to make use of Israel's healthcare system, but then too many terrorists have used that opportunity to smuggle bombs in.)
I disagree with your reasoning about why there is a conflict. Conflicts do not exist because two sides don't want to lose, conflicts exist because one side wants to win. Israel, and I say that as an ardent Zionist, would be perfectly happy with a draw. At any time during this conflict, from the very beginning to today, Israel was happy to accept an end of the conflict immediately without any changes of the status quo. That was true in 1948 before the original Arab attack (when Israel consisted mainly of the land the KNF had bought plus the Negev minus Jerusalem, most of which was already Jewish-owned), in 1967 when Jerusalem was divided between Israel and Jordan, and it is true today, when Israel controls all of Jerusalem, the West-Bank and the Golan. (Of course, a draw gets easier and easier for Israel, since the base situation changes with every win.)
Neither side wants to lose, that is correct; but that alone doesn't create conflict. I think conflicts exist because in every possible conflict there is one side that accepts neither loss nor draw.
Gedanken.
It's one of those thought experiments that makes people admit to themselves their true positions.
The other one I occasionally use is about dressing up as a Jew (with an Israeli flag) and visiting an Arab city vs dressing up as an Arab (with an Arab flag) and visiting an Israeli city.
Most people I have met who were, as they claimed, totally convinced that the Arabs want peace and that Israelis don't, suddenly had to admit that they wouldn't bet their lives on their conviction.
I would. (But then I have seen Arabs walk through Israeli cities demonstrating for the PLO. An they survived.)
I do not propose the bet any more where I offer to do exactly that in an Israeli city in exchange for my opponent doing the Arab city part because I don't want people to get killed over a bet.
both would. At least those not engaged in agressive attacks.
(retaliation is not agressive, but defensive.)
Israel usually doesn't even go for retaliation but actually tries to destroy the rocket launcher installations and weapons depots. In contrast to what so many think, war is expensive and switching off the terrorists for a few days is cheaper than retaliating against a population. Bombs cost money, if they are build to hit specific things.
If both Israel and Gaza would be in favour of this border being closed as I propose here (although this is sadly impossible), then the border wouldn't have to be closed at all.
(I also came up with a more violent version of this idea. In that version the border would act as a tele-porter array, shifting all incoming rockets so they would hit Riyad, the capital of Saudi-Arabia. I wonder whether these rockets would still be perfectly acceptable resistance if they hit Saudi-Arabia.)