Non-native speakers tend to say “happy hours” & “rush hours” but native speakers almost always say “happy hour” & “rush hour.”
I have offered an explanation that’s easy to understand and remember:
“happy hour” is like 限時搶購/歡樂時光/優惠時段 in Chinese & “rush hour” is like 尖峰時刻.
For a department store限時搶購 can be a period of one month. Usually a karaoke or pub will offer 3 to 4 hours as歡樂時光.
As for尖峰時刻, because it’s a nightmare, psychologically we want it to get over very soon, so we say “rush hour” instead of “rush hour.”