There is a somewhat confusing logic behind when the FOLLOW button is displayed on the search results hover panel (a.k.a document preview).

What I am talking about?
If you are building a solution that relies on the following of documents but you are using Yammer rather than the SharePoint social feed then you may be wondering why, from the search results hover panel, you can follow pages, users, sites, but not most document types.
NB. If you are finding that you can’t following anything, check that web scoped feature ‘Follow Content’ has been activated on each site which contains content you wish to be able to follow.
NB. You can still follow the document types in question by clicking ‘view in library’ and using the library item menu to follow.
In many cases, wanting both POST and FOLLOW doesn’t make a lot sense as a primary reason of following documents is to populate the activity feed which is not available when Yammer is being used as the enterprise social experience. As such, please consider why you want this behaviour at all. In my scenario the user’s list of followed documents is promoted to the home page and bookmarking documents is a key user story.
What is going on?
The search results hover panel is built from a number of display templates which you can read about in more depth here (TechNet) or here (Chris O’Brien) or many other places.
Importantly, there is a display template which defines the common actions (buttons) across the bottom of the hover panel and when to display them. The display template is called Item_CommonHoverPanel_Actions and can be found here:
Site Settings > Master Pages and Page Layouts > Display Templates > Search > Item_CommonHoverPanel_Actions.html
If you inspect this display template you will find an if else
block around the rendering of the POST and FOLLOW buttons. The logic can be summarised as:
The POST button is visible if Yammer is enabled and the result type supports it, otherwise the FOLLOW button is visible if the result type supports it, at no time will both buttons be visible.
If you download a copy of the display template HTML file, update it to remove the ‘else’ as in the code snippet below, and then upload it again, you will find the both the POST and FOLLOW buttons will be displayed in the search hover panel when supported. Success!
But is it okay update that file?
The short answer is yes. Take care as this file is used by every hover panel in SharePoint (to my knowledge, there may be some completely unique ones) and so changes could break something that isn’t obvious.
The major risk is that if Microsoft decide to update the hover panel which require them to produce a new version of the display template file (they have done this previously when introducing the POST button). In the case that you have modified this file, then your changes will be lost. This can happen without warning (unless you have a second tenant on first release to catch these issues before they hit production – you should be doing this!).
For very minor updates such as this, and to support non-critical functionality, it may be okay to make these changes and be prepared to re-implement them should Microsoft issue an update.
The alternative is to make a copy of the display template with a new name. This approach means that your changes will not get overridden but it also means that your solution will not get the updates that would otherwise be pushed to this file. We call this ‘customisation tax’ and it is a trade off as to which way you’d rather push changes.
In this particular scenario this latter approach is not very practical as every result type references the existing display template. You would be required to make copies of all the result type display templates that are applicable (possibly a dozen or more), and update the result types themselves to use your new templates. Unless you are bypassing result types and using a single display template for all results, this feels overly complex for such a minor change, but major changes will necessitate the effort.
EDIT: A colleague of mine, Luis Manez, pointed out that with a little JS you can force a custom hover panel to be rendered for all result types. You can read about it (approach one) and some other approaches to associating custom hover panels here (Elio Struyf).
Paul.