After a user installs my application, where in the app's install directory should I place information regarding 3rd party software (e.g. FOSS) licenses? Should I just append it to my EULA? Is there some sort of convention or standard that I should following to make it easily scan-able by license detection scripts?
You probably ought to do both - place it in your EULA as well as providing a
LICENSE.txt (or equivalent) file. That way, your end users are aware of the licenses prior to accepting the terms of your license as well as being able to go back and reference the licenses later.
Most packages place the
LICENSE.txt file in the application root folder, but to my knowledge there's nothing preventing you from putting it in a logical place. If there's a convention, it's to place the file in the root of the application folder.
If you have a large number of licenses, then you may want to create a folder underneath your application called
Licenses and list all of the applicable licenses.