What's the name of the point where you are closest or furthest from the ecliptic? Every 24 hour day, there is a point as the earth rotates about its axis, where a location on earth is the closest to the ecliptic and where it's the furthest. Do those two points have a name?

What I mean is on the plane of the ecliptic, as the earth rotates around its axis, a point on the earth at 45 deg north is going to hit a low-point perpendicular to that plane, and will hit a high point perpendicular to that plane.
I don't know of a standard term for that quantity, but I'd call it the ecliptic latitude of the zenith.
With north positive and south negative, this would reach a minimum at 6:00 and a maximum at 18:00 local sidereal time.
These correspond to local solar noon or midnight at the solstices and occur 2 hours earlier per month.

The vectors perpendicular to the ecliptic are called the ecliptic poles. The zenith only coincides with one of these on the Arctic or Antarctic circle, at sunrise (winter-spring) or sunset (summer-fall).