Rainbow

A rainbow (虹, niji) is a phenomenon in the Rebuild continuity closely associated with the deaths of the Angels.

Rainbow that appears following 4th Angel's death.

It is probably a reference to the rainbow that appeared after the Biblical flood:

I set My bow in the cloud, and it shall be for a sign of a covenant between Me and the earth.

It shall come about, when I bring a cloud over the earth, that the bow will be seen in the cloud,

and I will remember My covenant, which is between Me and you and every living creature of all flesh; and never again shall the water become a flood to destroy all flesh.

Genesis 9:13~15[1]

God's "bow" being a sign of a "covenant" between himself, Earth, and all living things recalls the mysterious Covenant with Lilith. It's been suggested that the rainbows appear in the wake of Angels' deaths (which unleashes "floods" due to their bodies dissolving into red fluid) as a sign that the covenant is being fulfilled.

A rainbow appears when the Tenth Angel falls in battle against Eva-01, in advance of its actual death. It's unclear what this deviation from the preestablished pattern means.

Furthermore, rainbows appear upon the destruction of certain Evangelion units, but there is no clear pattern. Eva-04's explosion in Evangelion 2.0 tentatively included a rainbow earlier in production, but this was omitted for the final film.

Rainbows
5th Angel's rainbow	6th Angel's rainbow	3rd Angel's rainbow	Three rainbows for 7th Angel's demise
Multiple rainbows circling around 8th Angel's cross	Rainbow at 9th Angel's death	Rainbow for 10th Angel	Two for Eva Mk.4B
One apiece for the Nemesis Series	12th Angel	Evangelion Mark.09	Eva 44A cluster
Four total for Eva 4444C

Aside from rainbows themselves, rainbow motifs are scattered throughout both Rebuild and Neon Genesis Evangelion.