I’m not sure that it would. Those are designed to indicate whether you have L1-L2-L3 or L1-L3-L2. I’d not expect to see a meaningful result for (say) L1-L2-L2.
The three-phase sketch’s installation notes tell you how to set it up to get the phase sequence correct. I suggest you download the sketch and the accompanying documentation
Update to 3-Phase PLL sketch - #21 by Robert.Wall
and have a careful read so that you can see better what’s going to be involved.
When you’ve identified the correct sequence at one point, a simple voltmeter will identify which phase any outlet or circuit is on - given a long enough test lead. Just measure the voltage between the unknown phase and the three known ones, when the answer is close to zero, that’s the same phase. When it’s close to 415 V, it isn’t. I’d expect to see a few volts when you’ve got the same phase. And remember to check that it’s live first.
From a point of view of personal safety, I’d expect all the outlets in one room, and certainly all those that are within reach of one another, to be on the same phase. If they’re not and there happen to be two faulty items, you stand to get a 415 V shock rather than a 240 V one. It’s something I’d check, and from what you write, you’ll be documenting it. Over time, I’ve documented everything like that in my house - it’s invaluable when you need to change or add something.