FormerlyHemlock
Hero
fyi, picking pockets isn't an attack or spell so would not break invisibility.
BTW, taunting (Swashbucklers w/ Panache) isn't an attack or a spell either, so a Swashbuckler 9/Wizard 3 can invisibly taunt away, basically guaranteeing disadvantage to all enemy attacks on anybody who can understand him.
There are a number of interesting things to do with one's action which are neither attacks nor spells. Laying caltrops, Long Death Monk's Fear ability, Channel Divinity, [arguably] grappling (PHB is very clear that "no attack roll" = "not an attack", though this is controversial because grappling is also called a "special kind" of attack (which isn't an attack?)), Hypnotic Gaze (Enchanter ability), etc. Many of them require the target to see you though, which is what makes Panache especially interesting, since it only requires the target to be able to see or hear you.