Hello Moeller1983 and welcome to Apple Support Communities.
I see you have a question about hard drive activity (specifically with the drive spinning) when Time Machine does not appear to be running.
Back up your Mac with Time Machine - Apple Support
It's important to keep in mind that there are Time Machine tasks that are not specifically backing up. This would include things such as identifying older backups which can be deleted if the drive is starting to get low on space.
If you want to get a snapshot of all the processes underway at any time on your Mac, you can get that via the Console app.
Console User Guide for Mac - Apple Support
Cheers.