What is the position if one cannot be in shul for Tachanun, with no sefer torah present , but is, for example , davenning at home in a room full of seforim.
Can one lower one’s head, or is this still not permitted ?
There are different opinions and customs regarding this. The custom among many is not to. See sources.
See Rema 131-2, M:B 131-11 and Shar Hatzion 9 brings different opinions however it would appear that he holds not to cover the face, and so says Tefilah K’hilchoso and Eishei Yisroel 25-10. This seems to be the minhag in the Lithuanian Yeshivos. Piskei Teshuvos 131-11 however says that the minhag is to cover, also see Orchos Rabeinu 1 pg. 67 that the Steipler did cover his face in a room that had seforim in it, see Halichos Shlomo (Tefillah) 11 ftnt. 37 that R’ S. Z. Auerbach also did, but only in a room in Yerushalayim, but not in other cities.