Nothing “shines” on the earth from the sun at night.
That’s as dumb as the old ethnic joke about the scientific team who is going to land on the sun, and avoid the heat by landing at night.
Even if the sun is not visible at “your location” at a given hour, neutrinos are passing though the earth and effectively coming “up” through the earth at night at the speed of light.
However, every radioactive isotope which undergoes a beta decay also emits a neutrino. No need to capture neutrinos from the sun, put a detector on the exterior wall of your local nuclear power plant reactor building and that is a much more effective capture geometry than the point source (sun) millions of miles away.
Except this whole thing is April Fools BS, neutrinos don’t interact with mass under the known “laws” of physics.