Whilst you've reached the top of the columned face of the building, you haven't actually completed your climb. Rising out of the domed roof of the exhibit hall is a tower atopped by a clock face and viewing gallery. That is your target - and it's about time you got there. It's very nearly time to put the plan into action!
Luckily this part of the journey is not up a sheer surface - there are gullies and windows embedded in the walls, according to the conceit of the architect. As you rise past them, you look in on the tower. It's structured oddly, in that it is completely hollow and floorless. The tower is intended to be looked up, from the floor of the main showing room. At the very top is a famed mural, which you plan to desecrate tonight.
No time like the present! As you reach the top of the miniature tower, climbing over its crenelated walls, you can see the faint outline of a windswept and ancient trapdoor. Despite the museum's recent renovations, this area was deemed unsafe to repair, rather ironically.