Sorry, but what? I don't see how it is relevant to the question asked in topic, which I answered.
Once again - to put the new template inside another one you need to use
<template YOURTEMPLATENAME> inside the other template, where
YOURTEMPLATENAME is the name of new custom template you created. It will put the code from
YOURTEMPLATENAME to the place where you inserted it.
So if the my_new_template contains this:
<tr><td class="trow2"><strong>Hello world</strong></td></tr>
And you'll put <template my_new_template> in index_birthdays:
<tr><td class="tcat"><span class="smalltext"><strong>{$lang->todays_birthdays}</strong></span></td></tr>
<tr>
<td class="trow1"><span class="smalltext">{$bdays}</span></td>
</tr>
<template my_new_template>
It will output:
<tr><td class="tcat"><span class="smalltext"><strong>{$lang->todays_birthdays}</strong></span></td></tr>
<tr>
<td class="trow1"><span class="smalltext">{$bdays}</span></td>
</tr>
<tr><td class="trow2"><strong>Hello world</strong></td></tr>
If you want the template to be under another templates in ACP, not in ungrouped, you need to write own plugin and insert it to the set you want with query (requires PHP and MySQL knowledge, look how is it done for example in MyAlerts), but I don't see the connection to the question asked in topic.