Full Drive Access has become a little complicated. Here’s the story...
The Mac App Store version of EtreCheck is limited by the Mac App Store sandbox. Many Mac App Store apps allow a partial escape from the sandbox by having the user save a reference to the root directory of the hard drive. Apple allows this, but does not encourage it. The command to access this needs to be hidden away in an app’s preferences. An app can’t demand it and has to provide functionality without it.
As of Mojave, Apple has extended the Mac App Store sandbox outside of the Mac App Store a little bit. Any apps running on Mojave need extra permissions to access certain protected directories.
So, if you are running the Mac App Store version of EtreCheck on Mojave, enabling Full Drive Access is a two-step process. Go to the EtreCheck menu and choose Preferences. Then choose the Privacy tab. There will be a button to enable Full Drive Access. If you click it, it will display a dialog with two Allow buttons. Click one button to allow EtreCheck to read the entire hard drive. Click the other button to open the Privacy pane in System Preferences and select Full Disk Access. You will have to manually add EtreCheck to the Full Disk Access list. Then, after quitting and restarting EtreCheck, it should have Full Drive Access enabled.
Note that EtreCheck uses the phrase Full Drive Access to account for this potentially two-step process to differentiate it from Mojave’s Full Disk Access. Confused yet?
None of this is related to permissions in the Finder or Time Machine.
And finally, there are some practicalities to worry about. Since an operating system function is required to make this happen, EtreCheck is dependent on the operating system functioning correctly. That doesn’t always happen. If you want to contact me using EtreCheck’s built-in support feature, there are a couple of tricks you can try to get it to work. There is even a Terminal command to reset it completely. It can be fixed, depending on how hard you want to work.