Word-of-mouth leads in Madison

A friend who works at a local manufacturer says there are openings not advertised online. I am in Madison, in case local advice matters. They like a brief email with a résumé. Does anyone have similar leads?

Visiting in person worked for a trades job. For office jobs, email was better.

A short email with two sentences about what you can do and your résumé attached worked for me. I followed up after a week.