Firstly, they are "two witnesses" with a corroborated testimony (unlike the witnesses who accused Jesus, for instance). Because they agreed, those who swore to keep the Law could be punished, excommunicated, or executed for breaking it.
Some have tried to fit the ten words to the five-fold Covenant pattern found everywhere in the Torah (and beyond) but the best solution I have found is the one from Moshe Kline at www.chaver.com, a Jewish scholar who follows the "scroll" division of the commandments (as Augustine). This means that our first two are combined into one, and our last is divided into two. If we read the laws as the warp and weft in fabric, we have "Adamic" laws as 1 3 5 7 9 (odd numbers) and "Evian" laws as 2 4 6 8 10 (even numbers, multiples of two - the Bride always "multiplies":
Adam/Priest/Head - - - - - - - - - - - - Eve/People/Body
False Words from gods - - - - - - - - - - - - False words to God
Working the Land (Sabbath) - - - - - - - - - - - -Honoring Parents in the Land
Murder - - - - - - - - - - - - Harlotry
Theft (false blessings) - - - - - - - - - - - -Legal Witness (false curses)
Coveting House - - - - - - - - - - - -Coveting Household
So the structure works from above to beside to below (from God down to offspring, past to future), and it follows the fivefold Covenant pattern:
Hierarchy (Man - these are the curses on Adam and Eve, land and womb)
Ethics (Sacrificial Law - notice that murder and adultery are strange knife and strange fire)
Sanctions (Blessings and curses when called to account by God)
Succession (offspring and the future - Adam as shelter - a tree of righteousness)
Then, left to right it is Adam - Eve - Adam - Eve, etc.
Finally, the words were written with the FINGER of God. Ten Words is ten fingers, two human hands, instruments of righteousness or unrighteousness. When Jesus broke bread, He would have used all ten fingers to tear it, picturing His imminent death under the curse of the Law.
"And Moses threw the tablets out of his hands..."
If the Adam/Eve priest/people idea is strange, it is simply the totus Christus. Also, the High Priest made two approaches to the Most Holy on the Day of Atonement, once for the priesthood and once for the people. We also see this in Abraham, who entered the land to sacrifice Isaac (firstfruits/priesthood) and then again to bury Sarah (offspring/people). It's everywhere - check it out in Daniel 7. We also see it in Jesus ascending into the cloud as "head" then four decades later returning "in like manner" for the sacrificial "body," the martyrs, fulfilling the vision in Daniel 7.
There's more in my book on Covenant structure.