seat, mat, occasion, place
席 centers on a designated spot for sitting or gathering: a seat, a mat to sit on, or a place at an occasion. The idea extends naturally to the event or place itself.
席 combines 广 (building) with a component representing a mat or cloth (巾) under a covering (廿), suggesting a mat spread inside a building for sitting. The modern form preserves this structure.
Under a roof (广), a woven mat (巾) with a cover (廿) is spread out: that is your seat at the gathering.
For セキ, imagine a second (セカンド) seat at the occasion: second -> セキ, and you take your place on the mat.
seat
attendance; presence; appearance
seat (esp. in public places or places with assigned seating); seating
parliamentary seat
absence; non-attendance
batter's box; one's turn at bat
guest seating (e.g. theater, stadium); passenger seat (e.g. taxi)
being present (at the same meeting, occasion, etc.); attendance (with); sitting with; sitting next to
empty seat; unoccupied seat
head; chief
full house; all seats occupied; fully occupied
taking a seat; sitting down (in one's seat)
impromptu; improvised; extempore; ad-lib; off-the-cuff
all seats
sweeping (over, across); conquering; overwhelming
entertainment hall (for rakugo, manzai, magic, music, etc.); vaudeville theater (theatre); music hall
sharing a table with someone you don't know (e.g. at a restaurant)
associate; junior; assistant; next in rank; runner-up
attendance; presence
leaving one's seat