Generally speaking, black pen or carbon ink pen is used to sign important documents. The reason should be that black ink can be kept for a long time. In case of accidents (for example, the black handwriting is still clear when the document is wet by water, and nothing else works), all documents should be signed with a black stylus.
Black ink pens or signature pens mainly contain carbon. Anyone who has studied chemistry knows that carbon is stable and not easy to be oxidized, so handwriting is preserved for a long time.