Re: Correction or have I misunderstood...?
At that distance the Earth does not eclipse the Sun completely so some of the Sun is always visible. However JWST orbits around L2 so Sun is likely never shaded for it.
Reason for L2 in fact is that Earth and Sun are both in approx same direction so you can put heat shield up and protect against heat from both the large objects at the same time (also Moon I expect). Anywhere else you either need to be too far from Earth which lowers bandwidth or you need two shields. So L2 is brilliant for this.