[kgwgk]

Let’s assume you’re at longitude 0 and noon happens for you at 12:00 (on average). If there were 24 timezones of exactly 15 degrees of longitude each there will be places at longitude +/- 7.4999 which are in your time zone where noon happens at 11:30 or 12:30 (on average) and never at 12:00. If you want to “fix” this problem you need to add timezones, not to mess wit the clock.

If you only care about your (latitude 0) time of noon which is given by that chart and you want to make it closer to 12:00 by splitting the year in “winter” and “summer” time (with only two changes in the year) you would have winter time from late-december to mid-june and summer time from mid-june to late-december and apply a time shift of about 10 or 15 minutes. This is just a guess, you may take that curve and optimize the timing and magnitude of the shift to approximate the curve with two constante segments. Or more that two, if you want.