We definitely know the motivation for disclosing the dragon: it was disclosed to build a tower. I don't know about the disclosure of the bones: that's going to take some more research (I'll update my answer if I find an answer).
Dragons
The story of the concealing of the dragons is recounted in the Welsh tale Llud a Llefelys:
"And the second plague," said he, " that is in thy dominion, behold it is a dragon. And another dragon of a foreign race is fighting with it, and striving to overcome it. And therefore does your dragon make a fearful outcry. And on this wise mayest thou come to know this. After thou hast returned home, cause the Island to be measured in its length and breadth, and in the place where thou dost find the exact central point, there cause a pit to be dug, and cause a cauldron full of the best mead that can be made to be put in the pit, with a covering of satin over the face of the cauldron. And then, in thine own person do thou remain there watching, and thou wilt see the dragons fighting in the form of terrific animals. And at length they will take the form of dragons in the air. And last of all, after wearying themselves with fierce and furious fighting, they will fall in the form of two pigs upon the covering, and they will sink in, and the covering with them, and they will draw it down to the very bottom of the cauldron. And they will drink up the whole of the mead; and after that they will sleep. Thereupon do thou immediately fold the covering around them, and bury them in a kistvaen, in the strongest place thou hast in thy dominions, and hide them in the earth. And as long as they shall bide in that strong place no plague shall come to the Island of Britain from elsewhere."
And the story of their "disclosure" is given both in Nennius' Historia Brittonum and in Geoffrey of Monmouth's Historia Regum. I'm going to quote from Geoffrey because I find it easier to follow:
Unto whom spake Merlin: 'Know ye not what it is that doth hinder the foundation being laid of this tower? Ye have given counsel that the mortar thereof should be slacked of my blood, that so the tower should stand forthwith. Now tell me, what is it that lieth hid beneath the foundation, for somewhat is there that doth not allow it to stand?' But the wizards were adread and held their peace. Then saith Merlin, that is also called Ambrosius: 'My lord the King, call thy workmen and bid delve the soil, and a pool shalt thou find beneath it that doth forbid thy tower to stand.' And when this was done, straightway a pool was found under the earth, the which had made the soil unconstant. Then Ambrosius Merlin again came nigh unto the wizards and saith: 'Tell me now, ye lying flatterers, what is it that is under the pool?' But they were all dumb and answered
{p. 169}
{marg The magicians dumbfounded}unto him never a word. And again spake he unto the King, saying: 'Command, O King, that the pool be drained by conduits, and in the bottom thereof shalt thou behold two hollow stones and therein two dragons asleep.' The King, believing his words for that he had spoken true as touching the pool, commanded also that the pool should be drained. And when he found that it was even as Merlin had said he marvelled greatly. All they that stood by were no less astonished at such wisdom being found in him, deeming that he was possessed of some spirit of God.
Additional Commentary
As a bonus, here's some additional commentary on the triad. First, Will Parker discusses the purpose of the triads:
Finally, the burial of the fighting dragons at the end of this episodes recalls the talismanic concealment of Bendigeidfrân’s mortal remains at the end of the Second Branch, or those of Gwrthefyr as described in the Historia. The subsequent unearthing of these protective talismans is often lamented in the Welsh tradition, and is often used to explain why later generations were unable to resist the threatening gormesoedd as effectively as their mythological ancestors. As such, these ‘fortunate concealments’ and ‘unfortunate disclosures’ play an important part in the meta-narrative of sovereignty, loss and eventual restoration which we have seen played such a central role in Medievel Welsh historiography.
(Will Parker, Mabinogion.info)
And here's a quote discussion the inclusion of a dragon burial into the triad we're discussing:
As Ifor Willaims showed, the story of the burial of the dragons as given in Lludd a Llefelys is so closely dependent on HB's account of their disclosure as to indicate that this tale was invented subsequently to the ninth-century redaction of HB. Is it possible that in the triad the burial of the dragons has supplanted a third story of human talismanic burial?
(Trioedd Ynys Prydein: The Triads of the Island of Britain. This is the canonical source of information about the triads. I would buy the book, but it's incredibly expensive.)
