True enough there wasn't any US embassy in Baghdad from 67 to 84. But that didn't mean there wasn't any contact more, especially with the war of aggression waged by Iraq against its neighbour in 1980.

I wrote about involvement "before and during the war upon Iran" - and "before" was incorrect, so far as government contact was concerned. Though I do have some doubts about whether Saddam would have risked this attack without some assurances about how the USA would view it.

However during most of the war American support for the aggressors was very significant indeed. It was very clear that an Iranian victory would not be accepted by America as an outcome to the war.

The eventual ceasefire happened in the wake of the episode where USS Vincennes shot down a civilian Iranian airliner, killing all 290 people abroad, which must have helped to get that message across to the Iranian leaders. (And I'm not assuming this was a deliberate act of policy aimed at achieving this effect - but it must have looked like that from Tehran, whatever the actual explanation might have been.)