My method here is pretty sketchy. Basically you want to get the eyeball onto the conveyor belt so that it generates a lot of spin, enough to knock a beam from the gap below right onto the switch.
Reader Seth sends in this alternative. A more reliable and much less clumsy solution than what I came up with!
Yashar Kamyar also sent in this solution:
Level 92 is popular! Yet another solution, this one from Luisa: