Here's how I made my opinion: https://en.wikipedia.org/wiki/Stroke_order#Stroke_order_per_... separates traditional stroke order, Taiwan, Japanese, mainland China and Hong Kong, and specifically talks about 𠂇, saying that the traditional stroke order differentiates its stroke order according to etymology and character structure.

Which in and of itself, is not sufficient, but is a strong clue.

Then, if you look up the seal script origins of 左 and 右, you find that the top-left part of the character comes from different directions: It comes from the left for 左 (https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/%E...) and from the right for 右 (https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/%E...). One way to look at it is that the descending stroke of 𠂇 in 左 is the arm, while it's the horizontal stroke in 右.

But at this point, that's mostly conjecture.

So the next step is to simply find how the characters were actually written by writers from far in the past. And it turns out there are such resources:

左: http://shufa.guoxuedashi.com/5DE6/

右: http://shufa.guoxuedashi.com/53F3/

This contains the characters as written from a lot of different material from different periods. And in those many instances of the characters, the way the two first strokes can be connected is a strong indicator of how they were written.

For instance, on 左, they connect on the top-right end, indicating the horizontal stroke comes first: http://pic.guoxuedashi.com/shufa/6t1/29792.jpg http://pic.guoxuedashi.com/shufa/6t1/29793.jpg http://pic.guoxuedashi.com/shufa/ks/R201308025_TM.TXT.0248.0... http://pic.guoxuedashi.com/shufa/sf26/r201509387.0252.9ea9de...

And on 右, they connect on the lower-left end, indicating the horizontal stroke is last: http://pic.guoxuedashi.com/shufa/xs/r201308029.0111.18[26288... http://pic.guoxuedashi.com/shufa/xsd1/r201308030.0150.23[3dd... http://pic.guoxuedashi.com/shufa/xs/r201308029.0111.16[24a6b... http://pic.guoxuedashi.com/shufa/xsd1/r201308030.0150.23[3dd...

You can't do such connections by writing the horizontal stroke first.

There are also examples of the horizontal stroke connecting to the 口 part, further indicating it's the second stroke: http://pic.guoxuedashi.com/shufa/xsd1/r201308030.0150.5[6f86... http://pic.guoxuedashi.com/shufa/xs/r201308029.0111.2[0a33aa... http://pic.guoxuedashi.com/shufa/xs/r201308029.0111.4[0a2633...

If you look at the pages linked above, you'll also find the names of those writers, which you can look up and check out some of them were living > 1000 years ago.

Funnily, there's this interesting exception of 左 with the horizontal stroke second: http://pic.guoxuedashi.com/shufa/sf26/r201509387.0252.9eb7a9...