You quite heavily are writing for yourself within the loose framework of the overarching plot. I personally wouldn't rely too much on cooperating with other people in these kinds of role-plays for anything more than a couple posts, because then you're hinging your activity on their replies and fore-planning instead of going at it boldly and alone on your uncompromised time, which is the one basic freedom of a sandbox role-play as opposed to a more traditional "read-and-respond" group interaction RP, where you have to read others' posts and react to them if you want the group to collectively and cohesively advance.
Unless you don't care about willy-nilly fading out as your interest wanes later in the role-play, you should probably create some semblance of an arc for your character and have some short-term goals to fluidly meet. Whether or not you have the motivation to follow through on your own is another matter altogether.
If the sandbox you sign up to doesn't have an active GM willing to stir up motivation and throw in events that players can gravitate towards to keep things fresh and exciting, or as an aid for their players who may be looking for something to jumpstart their character through a more "main story"-relevant excursion, then expect that role-play to just be par for the course until you tire of or forget about it, honestly.
* Walks into [Tavern]
Greetings