To fully understand link below, there are a few things you need to know:-
https://earthsky.org/?p=3787
Our Calendar was born in 1582,
midnight was calculated by sundial method during this period, so to find midnight on 1st January at your location will not be the same as it is today, with whole area's having the same time, every town had "Local Time" as explained by Bristol Time" below:-
https://greenwichmeantime.com/articles/clocks/bristol-time/
Please note that i know most astrologers know this, i'm just explaining to those who don't, i'm not patronizing!
There are obviously two hemispheres, the Southern Hemisphere shows stars culminating at True North and some parts have Daylight Saving Time on 1st January during this time, like below:-
https://www.timeanddate.com/time/zones/aedt
The Northern Hemisphere doesn't have Daylight Saving Time during this time, but stars that culminate do so at True South, being the M.C.
Don't look for Sirius on the M.C. by projected measure (14*22' Cancer), it isn't accurate by astronomy or paran, please read below:-
https://astrologeratlarge.com/resources/articles/the-ecliptic-and-nothing-else/
Have you lost the will to live yet?
There is an easier way to do the sundial method by using an astrology wheel, get the Sun on the Nadir, or near to it, where you live on 1st January, this should be approx. midnight what people would calculate midnight with regarding New Year 200 years ago, Sirius should be approx. 10 degrees Cancer, the time now will not now show midnight.
Hopefully where you are at New Year doesn't have light pollution or cloud, astrologers in Australia have a better chance of seeing this as it is Summer.
You need to buy an app for your phone and adjust it to True South for Northern Hemisphere and True North for Southern Hemisphere, don't leave it on magnetic bearings or you will get the wrong bearings, link below will explain:-
https://www.youtube.com/watch?v=qIzkWuoqfpw
So after you have used your astrology programme to place the Sun on or near the Nadir at your location, and the M.C. is pointing at approx 10 degrees Cancer it will give the sundial local time for New Year, it will be before or after midnight.
This is the time you need to go out in the garden and look either True South or North which depends on what hemisphere you live in.
Look from the horizon straight up and you will see Sirius so make a wish!
https://www.youtube.com/watch?v=pguMUFyJ3_U
Please ask questions if you don't understand.