Usually placed after another verb to mean, "he (did x) all night". Literal meaning "until dawn, until morning": "he did x, and then it was morning." The person of nyemesap will match the subject of the previous verb, which can optionally take the same-subject suffix -ch or -k.
The daytime equivalent, "does x all day" is 'enyaa wehap, following the same rules.
Nyemsap is a common word for "it is morning" outside of 'Iipay, leading to nyemsapm "tomorrow, tomorrow morning" and nyemsaplly "in the morning", and nyemsapm nyakumakm "the day after tomorrow".
Written nemesap in Mesa Grande dictionary. Here sounds like nemesap in the first repetition, but the second may be more like nyemesap, which Cuevas clearly says in other recordings. Also exists in Tiipay as nyemsap and other variations.
Compare to nemeshap (nemeshaap) "is white"