You do not mention if your research students are graduate or undergraduate students.
First consider the extent to which career services at your university may or may not be helpful for your students. For instance, it may be helpful for resume and cover letter writing or interview strategies. However, it is designed for the whole student body and many not be helpful in pointing students in a specific discipline into a career path. So, they may not value career services as a resource for learning about future careers.
Second, it may be that your students have a narrow definition of what types of jobs there are in your field or what type of work is involved with different types of jobs. Your students may be open to learning more, but are unsure what questions to ask or where to research job opportunities. This may also be why students are more likely to look into job opportunities later in their education, than early in their education. They know more later about the field.
One suggestion to improve the process is to organize a seminar that includes faculty in your department and local professionals in your field to talk about careers in your field. Students will find this more inspiring and can learn more. You can make this a regular event (annual, each semester) and rotate the panelists so that students can see a variety of job opportunities and perspectives. I've seen this done in several disciplines and students seem to appreciate it. Also, since the panelists are basically discussing their own experiences, there is minimal prep for the people who volunteer.