Is there a way to force enable Reader View in Firefox on pages where the icon doesn't appear?

Solution 1: The Best One

You can try installing Activate Reader View, an add-on for Firefox that will force reader view even if the icon is not displayed.

This add-on adds a button to the toolbar. Clicking on it will (force) activate Reader View even if the icon in the address bar is not present.

Technically this Add-on prepends "about:reader?url=" to the current tab's address.

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Solution 2: Manual

Use Reader View on any site/webpage by adding below prefix to the url in the address bar:

about:reader?url=

For example, to view https://example.com/page1.html in Reader View,
enter about:reader?url=https://example.com/page1.html in the address bar and proceed.

Note: Doesn't work always.

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Solution 3: For older version of Firefox

Install Pentadactyl add-on for firefox and create a custom command:

:command reader execute "open about:reader?url=" + content.location.href

And then you type :reader to get the Reader View.

You can also map a keyboard shortcut to your custom command like so...

:nmap :reader

A simple Ctrl + R will force Reader View.

Note: Pentadactyl is (probably) no longer in development. Last release was in March 15, 2014 and works with Firefox 24.0 - 31.*

I added the following to my userChrome.css file:

#reader-mode-button { 
    display: -moz-box !important; 
    visibility: visible !important;
}

This makes the icon in the address (aka awesome) bar always be displayed. Clicking on it in a page that isn't an article probably won't work. But it ensures that I can go to reader mode quickly on any page where it does work.