Without having any intel, just pure speculation, I think the difference in the administrations is whether or not israel decides to take further action in Iran. If the USA has a weak President, then they absolutely keep going, full force. If it's Trump, I think they show restraint.
If President Trump gets re-elected, the changes for a long term solution go up immensely. For one thing, Trump has already demonstrated willingness to stop funding both
UNRWA (i.e. Hamas and Hezbollah) and the Palestinian Authority (Fatah), both of which are scams that use our money to perpetuate the conflict,
kill our people, and work against our national interests.
A lot of countries are really tired of Iranian-sponsored Palestinian terrorism. But they need strong American leadership, political support, and military support to do anything about it. The Abraham Accords were implemented during the Trump administration. A whole lot of countries had, or were about to, normalize relationships with Israel. There is an argument that Hamas' October 7th attacks happened when they did in order to spoil that process.
Countries like Egypt, Bahrain, Morocco, etc, have already normalized relations with Israel. Under a Trump administration, other Arab and Muslim countries such as Saudi Arabia will follow suit. Additional pressure will then be on Qatar to stop supporting terrorist organizations, which will lead to further degradation of Palestinian terror groups and their "from the river to the sea" goals. They all know that they are better off with Israel than with the chaos (and loss of economic activity) that would result from Israel's destruction. That, combined with their mistrust and sometimes outright hatred of Iran, could set the stage for the Palestinians finally getting their own, viable, and peaceful(ish) state.
Trump is going to be spending most of his time trying to unravel the Ukraine problem, I don't think he's going to pressure Israel the same way that a Harris administration will. In fact, one reason they are doing what they are doing now may be because they worry about what will happen politically if Trump *doesn't* win, not if he does.