빠지다 here is dropping out, stepping away, clearing off. -고 puts the action first: 개인 사진만 찍고 빠지는 관광객 'a tourist who just takes a solo photo and clears off', 기획만 하고 빠져 주시는 거네 'so he just plans it and then steps back'. 치고 빠지다 'hit and run' is a set phrase for striking then withdrawing, and 낄 때 끼고 빠질 때 빠져야 해 is the proverb-like 'you have to know when to join in and when to back off'. One line uses another sense — colour draining out of bleached hair.