Ok this is confusing. My investigator is on Arkham with a Nightgaunt when the 'Arrests Made in Murder Case" mythos card is drawn. The nightgaunt's reckoning effect moves it and the investigator to space 5 (city) and the investigator is delayed. The investigator then fails the influence check during the mythos event and gains a detained condition. So what happens during the next round? Does the detained condition prevent the investigator from "standing up" and ending the delayed condition during the action phase? During the encounter phase does the investigator encounter the nightgaunt or flip and resolve the detained condition, or both? Any help is appreciated.

Detained does not prevent standing up the investigator. Delayed does mean you cannot attempt the local action to get rid of the detained condition before the encounter phase.

During the encounter phase, follow the instructions on the delayed card as it says you can have no other encounter.

Detained does not prevent standing up the investigator. Delayed does mean you cannot attempt the local action to get rid of the detained condition before the encounter phase.

True. Please remember, as Ricedwlit pointed out that getting rid of the Detained condition is a local action: others can help you, even if you cannot attempt this by yourself due to being Delayed.

Thanks for the clarification.