Precisely three third party candidates have won any EC votes in the last century: George Wallace, Strom Thurmond and Robert La Follete. Follete won Wisconsin, and the other two unsurprising only won states in the deep south.
The likely "best case" scenario would be something like the 1912 election, which was essentially a three way race between former Republican president Teddy Roosevelt running third party against the incumbent Republican Taft, and the Democratic challenger, Willson.
Willson won 41.8% of the popular vote, and 81% of of EC vote. Taft got 23% of the vote, and managed to carry Vermont and Utah. Roosevelt got 27% of the vote, and carried 6 states. Eugene Debs didn't win a single state with his 6% of the vote - and its worth noting that the last time a third party candidate did as well as Debs was Perot, back in 96.
A majority of the country voted for a current or former Republican president, yet the election was a land slide for the Democrat in the EC.
Because of the structure of the EC, third parties are either irrelevant protest votes (such as the south protest voting for segregationists) or they blow up in your face. Why would this time be different?
Edit:
One significant problem with a pro-Palestinian third party revolt against Biden is that Democratic support for Palestinians isn't anywhere near high enough for a universal revolt against Biden on that issue. It'd just be begging for a repeat of 1912.
Netanyahu's poll numbers are pretty rock bottom among Democrats, but a majority of older Democrats see Israel as a legitimate state with an unfortunately far right current government that's going too far in their current war against a terrorist organization. They're not looking for a free Palestine that stretches from the river to the sea.
