Architects participate in this test by building one or more statues in honor of Thoth, who gave us the knowledge of geometry. The statues should have a significant cost to build, something in the same league as the Octec statues but without the crystals.
Each statue claims an area of land around it, using the same formula as the Test of Towers. This area is shown (only to the statue's owner) as a percentage of the area of Egypt. Unlike Towers, the statues never go poof and are subject to the normal ownership and salvage rules of Egyptian law.
Once per week, the highest-scoring statue whose owner has not yet passed is declared victorious, and its owner passes the Test of the Lonely Statue. Note that statues whose owners have already passed (and guild-owned statues) are not eligible for victory, and are skipped for purposes of finding the highest-scoring statue, but they will still claim land and affect the scores of statues around them.
I've always liked the "game" aspect of the Test of Towers, where architects compete directly against each other in a contest of cunning and productivity. The Lonely Statue test creates a similar game on a longer, more strategic time scale. Since only a single statue wins (the scores of statues with the same owner are not added up like with Towers) the nature of the game is different, too. Strategic moves could be to convince owners of nearby statues to salvage them, or to convince owners of statues near your competitors not to salvage them, or to contract with others to build statues in locations advantageous to you, or to build extra statues to take land from your most dangerous competitors. And of course to find the perfect lonely spot!
The test will not provide any knowledge about where competing statues are, other than the percentage displayed on your own statue. Sharing information about statue locations will be important, but sharing it with everyone (such as on the wiki) might not be in the architect's best interest. Statues should have a decent view range though.
I expect this Test to be self-balancing in terms of difficulty, because the objective is not to beat the highest historical score, but just the scores of the people currently competing. These scores will in general become lower and lower as more statues are built around egypt, but that just changes the "terrain" of the game and not its difficulty.