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Rosh Hashanah 16a.15 provides an example where חג can only mean the first seven days, since the pouring of water didn't take place on the eighth day (Sukkah 4:1). Since it's also interpreting Rosh ...
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#1: Initial revision
Rosh Hashanah 16a.15 provides an example where חג can *only* mean the first seven days, since the pouring of water didn't take place on the eighth day (Sukkah 4:1). Since it's also interpreting Rosh Hashanah 1:2, which you referred to, it's likely that the חג in connection to the judgment about rain is also referring to the first seven days. Obviously חג isn't limited to the first seven days, since you already have an example to the contrary. But I think this is enough to prove that it can't be assumed to include the eighth day, and probably doesn't include it in Rosh Hashanah 1:2.