Consider the insurrection statute (18 USC 2383):
Whoever incites, sets on foot, assists, or engages in any rebellion or insurrection against the authority of the United States or the laws thereof, or gives aid or comfort thereto, shall be fined under this title or imprisoned not more than ten years, or both; and shall be incapable of holding any office under the United States.
It seems to me that this contemplates two things: (1) that an “rebellion” or “insurrection” is an event that occurs and (2) that some people “engage”, etc. in the insurrection or rebellion.
So not everyone who attends an “insurrection” would be an insurrectionist (even if some of them commit other crimes). But there needs to be an insurrection for that person to engage in – some sort independent evaluation of the nature of the “event.”