To add twitter timelines or searches to a page, the owner of the account must create a twitter widget.
Log into twitter and go here: https://twitter.com/settings/widgets
Click 'Create New' and configure as needed.
When you click on the blue 'Create Widget' icon you'll be given some code which looks something like this:
<a class="twitter-timeline" href="https://twitter.com/NU_ITservice" data-widget-id="425662514961985538">Tweets by @NU_ITservice</a>
<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+"://platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}(document,"script","twitter-wjs");</script>
Copy it using "Ctrl+C", and return to T4.
Within T4's All Purpose Content Type, click on the Edit HTML Source icon.
A popup window will appear: paste the code into that, and it will then be embedded in the page.