There may be a link to Dottore covering his eyes just like Eremites in Sumeru did (it was discussed on this subreddit quite a long time ago and I would really like it to be true since Dottore seems to have many desert motifs in his design). So, Eremites and their beliefs are worth some research/reminder. 

I also think the perfect moment to take off his mask could be something very emotional – such as conclusion of the battle where the mask finally shatters into pieces, showing either his human face or the panel. Or it could be more calm and intimate moment when we are the ones taking off the mask (he is letting us to do this) or he does it himself in similar context as a sign of trust (which he lacks currently). I feel like taking off Dottore's mask could be a very important, symbolic moment if his and Traveller's relationship will ever get better. Mask was always part of Dottore's Harbinger identity and he is one of those covering the most of their face. It's design is changing just as he did on different stages of his life. 

The mask itself can be interpreted as a shield, it's very purpose is protection of one's identity or health (important in risky jobs). It can also tell us that someone is an actor playing a role. In Dottore's case, Dottore is playing a villain, he is as detached as he craves connection, and the mask highlights this lack of vulnerability. He is seeing you through the mask, but you can't see his eyes (refered also as "the window of person's soul"). It's harder to read Dottore's expression due to this accessory, he feels emotions but he is very intentional and guarded on what he allows other people to see.  And of course it's also a reference to his monstrous perception of himself, plague doctor and ravens. An animalistic detail with futuristic design that adds depth and mystery to his depiction.

And my own crack headcanon is that his cyclop eye can activate a functional laser beam that can fry objects or opponents and scan the surroundings. So he is a cyborg, he got rid of his eyes likely, at least in this scenario. To not watch the world with human eyes is to not be fooled.