noun, used as a suffix
Attaches to nouns to indicate doing something across, over, or through a physical barrier or intermediary. Common with 窓, 壁, 電話, 眼鏡, etc.
窓越しに外を見る。
Look outside through the window.
電話越しに彼の声を聞いた。
I heard his voice over the phone.
noun, used as a suffix
Attaches to time nouns to indicate a continuous span. Often used with 年, 夜, 一生, etc.
彼は一年越しの計画を実行した。
He carried out a plan that had been in the works for a year.
夜越しに働く。
Work throughout the night.
通し also means 'through' or 'throughout', but is more about continuous action or passage (e.g., 一日通し 'all day long'), while 越し emphasizes crossing a boundary or intermediary.
Derived from the verb 越す (こす, 'to cross over'), used as a suffix. The reading ごし is a rendaku form.