You can create a new background script with the following code:
chrome.browserAction.onClicked.addListener( function() {
chrome.tabs.executeScript( { file: 'inject.js' } );
});
Your inject.js
should stay as part of the extension, but you don't need to mention it in the manifest. This way, it will be run as a content script each time you press the extension icon. You didn't include the part of the manifest where you define the browserAction, but you just need to not specify a default_popup
.