Wiki doesn't have complete information atm about the requirements to access all of the Mysterious Pillars / Monoliths and I was curious to finally see all the visions myself before the Expedition, so I dug out my last pre-DC save and went to test them.
Silent Isle Pillars
- two sequential checks - first one just gates access to the second, main one
- access = psi empathy
- vision + psi ability (Bilocation) = 7 will + 35 base thought control
- wiki was unclear if these are separate checks for different rewards or not - it's one combined check to get both
- strange feeling debuff won't appear anymore after successful second check
- you get attacked by several doppelgangers on second check fail
Core City Sewers Pillars
- vision = 8 will
Oculus Crystal Mainframe
- two checks - one for mainframe menu access and second one for each vision
- access = psi empathy + 50 effective thought control / metathermics / psychokinesis (only one skill required, either one works)
- vision 1 = 70 effective psychokinesis
- vision 2 = 70 effective metathermics
- vision 3 = 70 effective thought control
Institute West Wing Monolith
- vision = 10 will
Deep Caverns Labyrinth Pillars
- vision = 8 will
Additionally, there's one more small vision:
Deep Caverns Faceless HQ Mindreader scan (when you enter Commander's building for the first time)
- vision = 80 effective thought control
- contrary to old Destroyor's steam guide, this does not provoke Faceless hostility and seem to have no impact on your standing with them
- (tested with psi empathy + up to 12 will / 215 eff tc, with and without all tc abilities learned, on char with all 3 cooperation encounters safely resolved)
All tests performed on current steam experimental build (v1.0.4.17).