This answer is only from the Theravada viewpoint. It's likely that you can find more diverse meditation techniques in Vajrayana.
Shambhavi Mudra is apparently an eyebrow center gazing gesture.
Agochari Mudra is apparently a nose tip gazing gesture.
While these are not found in Theravada Buddhism, the closest thing to it is parimukham. Please read this answer ...
Dukkha (seeing, knowing it, as well knowing a path) is cause of Saddha (surrender world toward liberation), Saddha causes joy, joy cause satisfaction, satisfaction cause stillness, stillness causes heal, heal causes concentration... vimutti, knowledge of release.
So here you are, good householder, now it's all about seeing Dukkha or not, to leave or stay.
Ven. Ananda was the Buddha's attendant and literally very close to him. In MN121, the Buddha teaches:
MN121:3.3: ‘Ānanda, these days I usually practice the meditation on emptiness.’
MN121 is a beautiful sutta and very inspiring. MN121 is the Cūḷasuññatasutta, the Shorter Discourse on Emptiness.
MN121 is not secret or hidden, but it can be confusing given ...
It is possible that the guru is explaining something called "suññatā cetovimutti" (空心三昧 kōng xīnsānmèi). You can read about it in the Godattasutta (SN 41.7). This sort of meditation is only practiced by the Arhats (i.e. the Buddha's "closest disciples"). From Pali Kanon: Manual of Buddhist Terms and Doctrines, the entry on "...