While not exactly explicit, Maimonides (Tzitzith 3:3), based on the baraita cited in the Talmud (Menachoth 43b), codifies that only the four outermost corners of a multi-cornered garment require tzitzith, without any disclaimer regarding garments that have eight or more corners:
(דברים כב יב) ״עַל אַרְבַּע כַּנְפוֹת כְּסוּתְךָ״ בַּעֲלַת אַרְבַּע וְלֹא ...
Refer to this website on the Shulchan Aruch HaRav here:
The scrupulous are particular to sleep with a Tallis Katan.1 The Arizal severely warned that one is to wear the Tallis Katan at all times, even at night.2 Practically, the custom of Chassidim is to be careful to sleep with a Tallis Katan.3 One may even initially put on the Tzitzis at night for this ...
Mishna Berura 21:15
שלא לשכב - ובכתבי האר"י ז"ל כתוב ע"פ הסוד שיש לשכב בלילה בטלית קטן
To not sleep - And in the writings of the Arizal it is written based on the mystical teaching [Kabbalah] that one should sleep at night while wearing a Tallit Kattan.