Apparently blocking the end of the trunk and then forcefully sucking or blowing air into the sinues such that the sides of the trunk collapse inward or bulge outward, as if a vaccum of sorts has been created. An audible sound may sometimes be heard as air is moved about in the nasal passages. Two examples we have are of musth males where this behavior seems to be part of a display and perhaps a prelude to a Musth-Rumble, while another is a male who has been engaged in elaborate testing of a female that involved putting his trunk inside her vagina and sucking. It is possible that this is what elephants are doing when they make the sound we call a Squelch.
References: Poole & Granli 2021. (Full reference list)
This behavior occurs in the following context(s): Advertisement & Attraction, Foraging & Comfort Technique