I think that you (and TMRE) are actually referring to planetary hours.
Many older magical texts will mention that a rite should be performed during the day and hour of some Planet. This is referring to the old system of planetary hours. Planetary hours use a sequence of Planets based on their observed speed and so assumed distance from Earth (at the center):
Saturn - Jupiter - Mars - Sun - Venus - Mercury - Moon
This was known as the "Chaldaean Order" of the Planets.
Planetary hours also use an old system of time keeping called "unequal hours". This means that there are 12 unequal hours of the day (from sunrise to sunset) followed by 12 unequal hours of the night from sunset to sunrise). Since the relative length of day and night changes throughout the year, you can understand that the "hours" will be of different length each day, hence "unequal".
The unequal hours are assigned to the Planets in the following way. Each day of the week is ruled by a Planet. In fact, our names for the days of the week are based on the 7 Planets of antiquity (sometimes by way of Norse deities):
Sunday -- Sun
Monday -- Moon
Tuesday -- (Tiw, god of war) -- Mars
Wednesday -- (Woden, trickster) -- Mercury
Thursday -- (Thor, lightning) -- Jupiter
Friday -- (Frigga, love) -- Venus
Saturday -- Saturn
The first unequal hour after sunrise on each day is ruled by the Planet ruling that day, e.g. the first hour of the day on Sunday is the hour of the Sun. The hours are then assigned to the 7 Planets in the Chaldaean Order given above, e.g. the second hour of the day on Sunday is the hour of Venus. This continues through the hours of the day and hours of the night, when a remarkable thing happens… The 12th hour of the night on Sunday is the hour of Mercury. The next Planet in the Chaldean Order is the Moon; so the next hour, the first hour of the day on Monday is the hour of the Moon!
Thus the 7 Planets give us not only the names of the days of the week, but also (through the planetary hours in their Chaldaean Order) the sequence of those days.
I don't know what hours based on the Signs would be. Does someone have a source for this?