The way to confirm this if others need it in the future would be to check the voltage at the starter when you are cranking the engine. You should have 12 volts at all times on the red wire and 12 volts on the other while you are cranking it.
Here is guide that will help with this.
https://www.2carpros.com/articles/starter-not-working-repair
Below is the wiring diagram that will help with this as well. However, normally when the starter is clicking rapidly the battery is drained so a load test would prove this out.
https://www.2carpros.com/articles/car-battery-load-test
Please let us know if you have other questions in the future. Thanks
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Monday, May 31st, 2021 AT 11:14 AM