[RPG] Blue Dragon Mask and Blue Dragon Sorcerer interaction

Draconomicon (v 3.5) has the best information I have found to piece together what dragons think like and for the most part they are like geniuses that feel a small urge to eat sheep and hoard treasure.

The most important element shaping a dragon’s outlook and state of mind is time. Dragons have no desire to live for the moment; they have a vast supply of moments stretching out before them. They do not worry about wasted time. If dragons have anything in excess, it is time, and they do not concern themselves with haste. Even the dullards among dragonkind seek to fill their time by exercising their minds. Solving puzzles is a favorite activity, though the form these puzzles take depends on the kind of dragon involved. Some, such as the bronze and the copper, seek out challenging puzzles of a benign nature. Others, such as the red and the blue, contemplate a much darker brand of conundrums. They plot ways to satisfy their greed, to defeat opponents, and to gain power over other creatures. Many scholars believe that dragons owe their natural aptitude for magic to the mental games they constantly play just to keep themselves occupied.

All true dragons have great patience. They seldom hurry or rush, because they believe anything worth doing is worth doing right. For a dragon, doing something right usually involves spending a long time (from the viewpoint of shorter-lived beings) contemplating the next step.

Are just a few examples from page 25 of the Draconomicon, seek that book for more info.

As for "what does this item make you think like" is somewhat of a different answer as noted in the comments below; the item does not turn you into a dragon with all of the ancestral memories that they would possess. Thus to answer that question "what makes someone dealing with dragons more compatible in mind set?", this would have to give you greater understanding of dragons, more then most; i.e. be closer in alignment to the dragon in question and also have great knowledge on the way said dragon would act or want. The Item does not grant all of these changes but in turn twists your mind so that you simply understand the body language of dragons innately, thus when interacting with them they seem to understand you better and as a result of this understanding you also would understand them to a much higher degree. If said dragon did not know of this item or that you possessed it, it would grant you significant advantage to social encounters with them.

I would describe to my player that while using this item, he suddenly feels everyone around him seems more blunt with their actions, their words seem so plain and open, every non-dragon seems much easier to read and I would grant them a circumstantial buff to their sense motive to any short-lived race. I do not believe they would even notice the item's influence when talking with dragons as it would feel natural.

No, but also Yes.

First, I'd like to point out the rules on wearing multiple items of the same kind:

Use common sense to determine whether more than one of a given kind of magic item can be worn.

A mask that "reshapes to fit the face and head of a wearer" sounds like a textbook example of an item where you can only wear one at a time, but I'll assume, as you state, that you have two heads, or some other way to wear two of these masks.

Even if you can physically wear both masks, magical effects with the same name don't stack, per the DMG Errata:

when two or more game features have the same name, only the effects of one of them -the most potent one-apply while the durations of the effects overlap.

Since abilities like Draconic Majesty and Dragon Sight are "game features with the same name", they don't normally stack.

None of this applies to the Dragon Masks in particular, since they have their own stacking rules described in the Rise of Tiamat book, on page 94:

If you try to "assemble" multiple dragon masks, they become the Mask of the Dragon Queen, and give you the properties of exactly one mask at a time, while giving extra Damage Absorption and Legendary Resistance.