Hi colinthewot and welcome to the forum.
colinthewot wrote:After many attempts to download Amplitube 4 Deluxe, it just doesn't appear anywhere on the computer.
I'm not sure what you mean by this, but here's somethings to check depending on what you've done so far:
Does the download not appear in your Downloads folder? You should get a zipped folder with an installer which needs to be run.
After you have installed, you need to run the Authorisation Manager and enter your serial number (from your User Area) to get the software to work fully.
If you've done this, you should be able to see AmpliTube 4 in your Apps folder, which you can use as a standalone. Be aware that it won't say Deluxe, this just refers to the amount of gear that comes as part of the bundle.
If you can see the App but just can't access it in Logic, you may need to reboot your Mac especially if you are running on Mojave.
If the above doesn't solve the issue, can you give us a bit more detail please. Tell us what you've done so far.