My take at the time..... conventional wisdom said if Carter got the hostages out, he'd get re-elected. A covert move was made to William Casey, Reagan's campaign manager, to deny Carter that success. Iran was persuaded not to work with Carter. The hostages were released at the same moment Reagan was being sworn in.
Later Casey said something like, "Mr. President, I didn't tell you earlier, but I made a deal with the Israelis. They own us because they can leak we traded the hostages for the Presidency. That's how the Neocon take over unfolded. Rumsfeld, the ME envoy, Perles, Cheney, Wolfowitz, Jean Kirkpatrick at the UN, William Bennet, Secretary of Education, on and on and on... all vociferously pro-Israeli. Israel got everything but the State Dept., who they were able to dismiss.
On the day Reagan entered his fourth quarter, when Israel now having more to lose than him, some obscure Beirut newspaper ran a piece about the Iran-Contra Affair. Next day, the story was front page in Paris, London, NY, LA, etc. and Reagan was captured fot his last two years.
Begin was able to say to Sec. of State Rodgers, forget your peace plan, we're not even going to discuss it with you.