How Do I Select the second instance of a certain block type
You could save that second text block's ID to a variable and compare against that in your text partial:

_entry.html:

{% set textBlocksIds = entry.postBody.type('text').ids() %}
{% set secondTextBlockId = textBlocksIds|length &gt;= 2 ? textBlocksIds[2] : textBlocksIds[1] %}

{% for block in entry.postBody %}
    {% include 'blog/blocks/_' ~ block.type ignore missing with {
        'block': block,
        'secondTextBlockId': secondTextBlockId
    } only %}
{% endfor %}


blog/blocks/_text.html:

{% if block.id == secondTextBlockId %}
    {% include 'blog/partials/_restaurants' %}
{% endif %}