Practitioners have argued about this for a long time, and there is no settled answer.
Both sides report the same kind of evidence. Some people find the solar-time chart describes them better. Others find the clock-time chart fits. Neither camp has produced a test that settles it.
The case for solar time: Saju is a system of natural rhythm. The hour branches were named for the sun's position, the Rat hour for midnight and the Horse hour for noon, and the classical texts were written when every town kept its own local time. On that view the clock is an administrative convenience, and the sun at your birthplace is the real reference.
In practice, most Saju readers in Korea do not ask where you were born. Korean almanacs (만세력) commonly apply a flat 30-minute shift for Seoul, so the Rat hour starts at 23:30 instead of 23:00, and leave it there. In China most chart apps default to Beijing time, with true solar time offered as an optional switch. Readers who correct for the full solar time are a minority, though a growing one.
The case for clock time (행정시간, 行政时间): people live by the time their society keeps. Work, school, birth records and every other rhythm of life run on the legal standard time, and a chart cast from that time describes the person as they live in their world. On that view the correction is unnecessary, and some readers add that the system has produced accurate readings for centuries without it.
True solar time (진태양시, 真太阳时) is the time shown by the sun at the exact place you were born. Noon is the moment the sun stands highest there. Clock time is different. It is one standard shared across a whole time zone, fixed by law, so for most birthplaces the sun's noon and the clock's noon are not the same moment. Three corrections separate the two.
Longitude. Every degree east or west of your time zone's standard meridian moves the sun's clock by four minutes. Korea keeps UTC+9 (meridian 135°E), but Seoul sits at 127°E, so Seoul's solar time runs about 32 minutes behind the clock. Beijing is 14 minutes behind. Ürümqi, on the same Beijing clock, is more than two hours behind.
Daylight saving time. If summer time was in force at your birth, the clock was an hour ahead of standard time. Korea used it in 1987 and 1988, China from 1986 to 1991, and most of North America and Europe still do. This calculator reads the historical time zone rules for your birthplace, so you do not need to know whether DST applied.
Equation of time. Because Earth's orbit is elliptical and its axis is tilted, the sun's noon drifts across the year by up to about 16 minutes against an even clock. This is the smallest correction, but it can still move a birth across a branch boundary.
Calculate your true solar time here and compare it with your clock time. If both fall in the same two-hour branch, the question does not matter for you. If they fall in different branches, or the correction moves your birth across midnight or past 23:00, read both charts and see which one describes you more accurately. Treat the chart that matches your life as your chart. The calculation above is exact; the choice of which time to use is yours.