I was of the belief that there would be no shadow whatsoever (no eclipse at all), but I'm finding that belief challenged.
The JWST would be in the Earth's antumbra if it went to the Sun-Earth L2 point. The JWST isn't going to the L2 point. It will instead be in a rather large halo orbit about the L2 point, one that has been specifically designed to not only preclude eclipses by the Earth but also by the Moon.
No eclipsing by the earth. It'll be in a wide halo orbit around ESL2, not at the point itself. Due to complicated math, being in a halo or Lissajous orbit requires less stationkeeping than trying to balance at the point itself.
ESL2 is only chosen as an orbit to ensure that the Sun, Earth, and the Moon are all on the same side of the telescope so that the sunshield can protect the telescope against thermal radiation from those as well in order to keep the telescope cool.
Lissajous orbits which are not halo orbits would lead to occasional partial eclipses, which is actually not desirable since the telescope is solar powered, and also you want it to go through as few unusual events as possible.