So I tried out myself a little experiment to determine if it was possible to differentiate mineral oil from DOT oil without relying on its colour.
Hypothesis
Since mineral oil is hydrophobic and DOT oil absorbs humidity, it should be possible to mix some water with them and observe a different behaviour.
- Water drops put in a recipient containing mineral oil should not mix with it and reach the bottom of the recipient.
- Water drops put in a recipient containing DOT oil should be absorbed by it and not reach the bottom of the recipient.
Experiment
- Safety first.

- Gather new mineral and DOT oil.

- Put some mineral oil and DOT oil inside a transparent recipient. Get also some tap water inside a small bottle.

- Put a few drops of water into each of the recipients.
Observations
- Water drops put into the mineral oil recipient go to the bottom quickly and keep their shape (1st picture). If shaken a bit, they regroup (2nd picture).

- Water drops put into the DOT oil recipient do not go to the bottom (1st picture) but rather get mixed with the fluid at the surface (2nd picture).

Conclusion
It is possible and pretty easy to figure out if an unknown brake fluid is mineral oil or DOT oil by mixing them with some water.
Bonus
We can also add much more water and observe something interesting. All the water is immediately going at the bottom of the recipient with mineral oil and completely mixes with DOT oil.
This is a picture right after adding a good quantity of water:

This one shows the same recipients but 6 hours later. Not much changed for the mineral oil but we can see that the DOT oil has had time to absorb the water and that little bubbles have appeared:

Edit
MaplePanda suggested (thanks!) to do the experiment the other way around by putting drops of oil into water instead. This is a good idea so I tried it and here is the result.
The recipient on the left is the one with a few drops of mineral oil. We can see a thin red layer on top and nothing elsewhere.
The recipient on the right is the one with a few drops of DOT oil. We can't see any yellow layer on top but rather tiny bubbles in the lower half portion of the recipient.

This method is as effective as the previous one at detecting the type of oil but is simpler as you only need a few drops of oil. Of course, I could have used way less oil in my first experiment, but still, I think this second method is superior.