Two-Headed Giant Constructed tournaments use Unified Deck Construction rules (see section 8.4).
In addition to cards banned in particular formats, the following card is banned in ALL Two-Headed Giant Constructed tournaments (Vintage, Legacy, Modern, and Block Constructed):
Sideboards are not allowed in constructed Two-Headed Giant tournaments.
Sideboards are disallowed because Two-Headed Giant matches are still best of 1 game. While this does impact the ability of players to functionally use cards like Living Wish that is an acceptable trade off. Aside from this, please remember that Two-Headed Giant constructed will be a particular format (Modern, Standard, Vintage!, etc) and as such is subject to those deck building restrictions. Additionally, Erayo is banned, no matter the format.