Whether you work in illustration part time or full time is not really a huge factor for agents. The topic never really came up when I was signing in with my agent. On our agency’s website we have this availability status on our profiles that lets clients know if an illustrator is either widely available, booked for the month but available the next, booked for 2 months, booked for 3, or even booked for the year, etc. And it’s totally up to the illustrator what to put up on their availability status. Also if you have a day job and already got an illustration job that’s taking most of your time, then you’re absolutely free to turn down any more offers. Even if you don’t have an illustration job, you have the freedom to turn down any new projects.