How many applications do I need before I can draw conclusions about whether my resume is working?

Use 100 applications as the baseline. The expected callback rate is 1–3%, so by 100 applications, you should have at least 3 recruiter calls. If you don't, your CSM will investigate timing first (were you applying within the first 24 hours?), then look at the resume. Don't make changes to your resume before you have enough data — you risk "fixing" something that wasn't the problem.