81:3 the appointed time = בַּכֵּסֶה.    The Authorized Version, i.e. King James read the time appointed, evidently as a loan word into Hebrew from Aramaic.  Jastrow gives the following entry: for "כֶּסֶה,כֶּסֶא" (pg. 652), "mark, distinction; marked, appointed time";  Jastrow cites this very Psalm text in the noun entry and the verb entry. The LXX seems to support an idea of the Aramaic word use: ευσημω, "clear, distinct", only it applies it to the Shofar, "distinct Shofar", or "clear sound of a Shofar", "with distinctness" (εν ευσημω), cf. Jastrow, "distinction" above.

Or alternatively, the word בַּכֵּסֶה means, "at the covering" more in line with the pure Hebrew root כָּסָה,  only pointed as a participle;  BDB gives "covering, garment, clothe, ... 4. cover, spread over";  The resulting translation would be, "Blow at the new moon, a Shofar, at the covering with light, for the day of our feast."

The poetic idea of the Psalm, then might be that the moon is receiving new clothing, i.e. the lighted crescent after being naked (i.e. dark).   The idea of light being a covering is illustrated in Numbers 9:15, where the pillar of fire covered the tabernacle.  See also Habakkuk 3:3, "His splendor covers the heavens", evidently lighted objects showing the glory of the Almighty.  Also texts, use this verb of covering nakedness.  A dark moon is a naked moon.  See Ezekiel 18:16.  It then begins to receive a covering at the new moon.

The basic sense of the Hebrew always seems to be something that covers over something else, and not necessarily to make the thing covered totally opaque.  For instance, Num. 22:5 describes the people that "cover the eye of the land";  surely the land is not made invisible, though in some cases the word is used where the thing covered is no longer visible. 

It has been suggested by some that the word here means "concealment", and that it therefore refers to the conjunction of the moon with the sun.  Out the uses where the sense "conceal" works in the context, the idea is clearly not a technical sense of "conjunction".  It is simply some kind of covering or hiding.   Since there are no examples of it clearly meaning "conjunction" in the modern sense, it is speculation to say so.  And, this idea is squarely contradicted by Genesis 1:14, "Let there be lights ... for signs, and for seasons, and for days and years".  It says "lights".  A dark moon is not a light.  It is between the old light and the new light.  It cannot be "for signs" until the light is renewed.

Also to consider is that in Revelation 12, the signs "appear" first, and then the Messiah is born.  Messiah is born on the day that follows the appearance of the sign, and not before the sign appears.  The sign value is totally lost otherwise.  Therefore, the day following the sign is Yom Teruah, and not the day before the sign.