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Simple method, but do you realize that noon is affected by equation of time which changes several minutes over the year ? Any astronomy app will show the true noon time on this day for your location.
Where is is meant for ? You don't have unobstructed view to the pole star in the south ?
If you have an EQ mount with setting circles and a star charting app displaying ephemeris it is much simpler. I can align the scope using a two star alignment using the Sun and Moon or Venus. When the latter two are not available, I use the zenith as 'star' with hour angle of zero and declination equal to your latitude.
It even works on a simple balcony which just fits your scope and tripod.
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