<div id="tab1">stuff</div>

<div id="tab2">stuff</div>

</div>

This worked fine. The contents were in:

field--field-tab1--my-content-type.tpl.php

I then split the contents of the second tab off into a template for the second field. This field has the same field display settings in the content type as the first field. The files now look like this:

field--field-tab1--my-content-type.tpl.php

<div id="tabs">

<ul>

  <li>tab1</li>

  <li>tab2</li>

</ul>

<div id="tab1">stuff</div>

field--field-tab2--my-content-type.tpl.php

<div id="tab2">stuff</div>

</div>

The second template is not picked up at all (tried using die() to be sure), so I get the tabs, with only the first being operational with content. 

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