Hi Kevin,
OOB, the search lookup is on the home web template which is controlled by the setting 'Search/Enabled'. And it works as mentioned by you i.e. on click/ enter redirects to search/?logicalname...
Below is the oob home web template... take a copy of your current home web tenplate and try this to see if it works. If it does work then you can compare the versions and figure out what is missing... hope this helps.
Home Web Template
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{% assign forums_sm = sitemarkers["Forums"] %}
<section class="page_section section-landing">
<div class="container">
<div class="row ">
<div class="col-md-12">
<h1 class="section-landing-heading">{% editable snippets 'Home/Title' default: 'Contoso' %}</h1>
<h2 class="section-landing-sub-heading">{% editable snippets 'Home/Subtitle' default: 'Customer' %}</h2>
{% include 'Search' %}
</div>
</div>
</div>
<div class="layer_down"> </div>
</section>
<section class="page_section section-knowledge">
<div class="layer_up"> </div>
<div class="container">
<div class="content-home">
<h2 class="blue_border">{% editable snippets "Home/MostPopularHeading" default: resx["Most_Popular"] %}</h2>
{% include 'Knowledge Management - Most Popular Articles' showdescription: true %}
</div>
<div class="row sidebar-home no-lr-margins">
<div class="col-md-4">{% include 'Knowledge Management - Most Popular Articles' showdescription: false %}</div>
<div class="col-md-4">{% include 'Knowledge Management - Most Recent Articles' %}</div>
<div class="col-md-4">{% include 'Knowledge Management - Top Rated Articles' %}</div>
</div>
</div>
</section>
<section class="page_section section-sub-landing color-inverse">
<div class="container">
<div class="row">
<div class="col-md-4 text_center-mobile">
<h1>{{ forums_sm.adx_name | escape }}</h1>
{% editable snippets "Forum/HomeDescription" %}
<a href="{{ forums_sm.url | h }}" class="btn btn-info-home btn-lg-home" title="{{ snippets['Home/ViewMoreButton'] | default: resx['View_More'] | h }}">{{ snippets['Home/ViewMoreButton'] | default: resx['View_More'] | h }}</a>
</div>
</div>
</div>
</section>
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