I have eclipse installed (I guess automatically from when I installed the AndroidSDK), but I've never once opened it. You don't need to in order to build Android versions in Unity.
What are you opening Eclipse to do?
Make sure you've installed;
Toos/ AndroidSDKTools, Platform-Tools, and Build-Tools for the APIs you want to install.
And in the section for each API you support, make sure all elements are installed.
And in the Extras section at the bottom, install whatever is relevant for your needs.