Yes, my PHP code interpolates an approximation of the equation of time. The file name on the server is “eot.php” as I recall. It gets UTC from the server, adjusts for the longitude of my house, and adjusts for the equation of time at the moment. I think it is generally accurate within a few seconds. So it is a 24-hour sundial, just easier to read more accurately. “Mean solar time” is no fun. Bu5 I don’t need to use it, since I have an app on my phone and Apple Watch that gives current solar time.
Back before I gave up on my lawn mower and hired a yard guy, I took sun time into account when considering when to do yard work. The day we change back to standard time is usually the day here when sun time and clock time get the closest, about six minutes apart. Right now, as I said, it is about an hour and a half.
When I got back from Italy in the fall, after going back and forth between time zones and into standard time, I decided to leave the Roman shades up in my bedroom to help me readjust to EST. There are three large windows facing north with woods not that many feet away, so a glorious view in the fall anyway. I have left them open, and now with nothing scheduled, I find myself operating more or less by the sun more than the clock.