For example, were there any interactions between Nixon's campaign of 1968 and the North Vietnamese, or the Reagan's campaign of 1980 and the Iranian revolutionaries holding Americans hostage? Or perhaps other examples?
I cannot answer this in full for all US elections because that is not my field of knowledge.
From my own field however, I can say that in the 1968 US presidential elections, the Soviet Union tried to interfere in it. Initially the Soviet ambassador was instructed by the Soviet Foreign Ministry to offer Democratic candidate and Vice President Hubert Humphrey any kind of help he asked for, including money. The offer was made at an informal dinner between Humphrey's family and that of the Soviet ambassador. The ambassador was however careful in his formulations so as not to cause a potential diplomatic scandal.
The Soviets feared Nixon as an anti-Communist Hawk, while the Kremlin had set as its goal to reach agreements with the US. The domestic prestige of the new Soviet leader Brezhnev was thus at stake to get an agreeable president elected.
The KGB in the meantime had established contact with the Nixon campaign through Henry Kissinger. Working as academic and foreign policy advisor to Nixon, Kissinger was approached by a Russian reporter for the Novosti Press Agency, Boris Sedov. Russian news reporters were more often than not a cover for KGB officers. Sedov knew Kissinger from before he entered politics, but now made use of this contact to obtain information on Nixon's intentions towards the USSR.
When Kissinger hinted that Nixon was pragmatic and that his anti-Communist rhetoric was just rhetoric. Kissinger was probably aware that the reporter was linked to the KGB, and Nixon probably instructed Kissinger to pass on his willingness to improve relations. Several unofficial letters expressing mutual willingness to cooperate in the future were sent between Nixon and Brezhnev through Sedov and Kissinger. These contacts lasted for several months.
Recommended literature & sources:
Anatoly Dobrynin, "In Confidence: Moscow's Ambassador to America's Six Cold War Presidents"
Oleg Kalugin, "Spymaster: My Thirty-two Years in Intelligence and Espionage against the West"
Christopher Andrew & Vasili Mitrokhin, "The Sword and the Shield: the Mitrokhin archive and the secret history of the KGB"