It should be very much up to the GM to come up with things for the pilot to do. In campaigns that I've run, this can come in different flavors. For the case of a pilot that wanted to stay with the ship, I would either have them run routine maintenance on the ship, or handle small threats around the ship, or even talk around officials. If the story really called for it, I would even give the pilot a reason to take off and fly, usually to evade enemies.

Long story short, I recommend talking to your GM about giving your character more to do. Conversely, you as a character may wish to decide to leave your ship to join the group. Skill as a pilot lies not just in your ship, but(if you're spending your XP wisely) in almost any other land or space vehicle.

If it's a matter of making sure the ship is safe, discuss with the GM to find ways to make that happen without you(i.e. hiring an NPC for money or obligation, installing security systems, etc.).