The tongue is nearly flat, and is pulled back rather than down as in the postalveolar clicks, making a sharper sound than those consonants.
The tongue makes an extremely broad contact across the roof of the mouth, making correlation with the places of articulation of non-clicks difficult, but Ladefoged & Traill (1984:18) find that the primary place of articulation is the palate, and say that "there is no doubt that [ǂ] should be described as a palatal sound".
The symbol in the International Phonetic Alphabet that represents the place of articulation of these sounds is ⟨ǂ⟩, a double-barred vertical bar.
This base letter is combined with a second element to indicate the manner of articulation, though that is commonly omitted for tenuis clicks.
[1] In official IPA transcription, the click letter is combined with a ⟨k ɡ ŋ q ɢ ɴ⟩ via a tie bar, though ⟨k⟩ is frequently omitted.