Just a note about the specific time: the Earthly Branches are as opaque to modern Chinese readers as they are to hanja-literate Koreans, i.e. extremely so. The link between what was originally "axe" 戌 to the 11th of 12 points (hence the 7-9pm slot of the day, the 11th 2-hour period counting from midnight to midnight) is not common knowledge, and is under some debate amongst historical linguists.
One view gaining traction comes from the association of the Earthly Branches with the 12 animals of the East Asian zodiac. This association is first clearly attested in the 日书 of the Qin dynasty. The evidence for some of these associations points to an Austroasiatic (also known as Mon-Khmer) origin for the association. The strongest associations are:
- 丑 Standard Mandarin Pinyin chǒu, Middle Chinese (Pulleyblank) trhjuwX, Old Chinese (Baxter-Sagart) * [n̥]ruʔ. The word buffalo (as opposed to ox, strictly speaking): Modern Vietnamese trâu, Proto-Vietic * c-luː , Muong tlu.
- 卯 Standard Mandarin Pinyin mǎo, Middle Chinese (Pulleyblank) mæwX, Old Chinese (Baxter-Sagart) * mˤruʔ. The word cat (which is traditionally used in the Vietnamese zodiac as opposed to rabbit in the Chinese and Korean zodiacs): Modern Vietnamese mèo, Proto-Vietic * mɛːw,
However, the link between 戌 and dog via a phonetic Old Chinese (* s.mi[t]) to Proto-Vietic (* ʔa-cɔːʔ) connection doesn't remotely look like it will work out.
That aside, it seems clear that 威 is an ideogrammic compound of 戌 and 女. Its positive connotations seem to go back to at least as far as the Classic of Poetry of the early Zhou dynasty.
Interestingly, the Shuowen Jiezi of the Han dynasty basically defines 威 as the same as 姑, the latter of which it specifically defines as "夫母也", that is to say, one's husband's mother (the use of which is obsolete in modern standard Chinese; 姑姑 has shifted to paternal aunts, the use of which is also current in Korean 고모). Knowing how 시어머니 treat 며느리 may give you a clue why this character came to mean what it does. Or it may just be a folk etymology.