How to include custom search template in theme search.php

Try use this:

$options = get_post_meta($_GET['formid'], 'awqsf-relbool', true);
if(isset($_GET['wqsfsubmit']) && $_GET['wqsfsubmit']==$options[0]['button']){
include(TEMPLATEPATH . '/search-phones.php');
}else{
include(TEMPLATEPATH . '/search.php');
}

Updated with this but no success. Here is my search.php and i added this in line 70. May be some syntax irregularities causing the codes showing along with results. the URL also looks quite weird. Like this:
https://www.cellularism.com/?s=8db0521a46&formid=2298&taxo%5B0%5D%5Bname%5D=phone_device_type&taxo%5B0%5D%5Bterm%5D=smartphone&taxo%5B1%5D%5Bname%5D=phone_brand&taxo%5B1%5D%5Bterm%5D=nokia&taxo%5B2%5D%5Bname%5D=phone_weight&taxo%5B2%5D%5Bterm%5D=wqsftaxoall&taxo%5B3%5D%5Bname%5D=phone_thickness&taxo%5B3%5D%5Bterm%5D=wqsftaxoall&taxo%5B4%5D%5Bname%5D=phones_display_type&taxo%5B4%5D%5Bterm%5D=wqsftaxoall&taxo%5B5%5D%5Bname%5D=phone_display-size&taxo%5B5%5D%5Bterm%5D=wqsftaxoall&taxo%5B6%5D%5Bname%5D=phone_display_resolution&taxo%5B6%5D%5Bterm%5D=wqsftaxoall&taxo%5B7%5D%5Bname%5D=phone_pixel_density&taxo%5B7%5D%5Bterm%5D=wqsftaxoall&taxo%5B8%5D%5Bname%5D=phone_cpu_cores&taxo%5B8%5D%5Bterm%5D=wqsftaxoall&taxo%5B9%5D%5Bname%5D=phones_operating_system&taxo%5B10%5D%5Bname%5D=phone_processor_speed&taxo%5B10%5D%5Bterm%5D=wqsftaxoall&taxo%5B11%5D%5Bname%5D=phone_built_in_storage&taxo%5B11%5D%5Bterm%5D=wqsftaxoall&taxo%5B12%5D%5Bname%5D=phone_ram&taxo%5B12%5D%5Bterm%5D=wqsftaxoall&taxo%5B13%5D%5Bname%5D=phone_primary_camera&taxo%5B13%5D%5Bterm%5D=wqsftaxoall&taxo%5B14%5D%5Bname%5D=phone_secondary_camera&taxo%5B14%5D%5Bterm%5D=wqsftaxoall&taxo%5B15%5D%5Bname%5D=phones_network&taxo%5B16%5D%5Bname%5D=phones_multiple_sim&taxo%5B17%5D%5Bname%5D=phones_video_recorder&taxo%5B18%5D%5Bname%5D=phones_sensors&taxo%5B19%5D%5Bname%5D=phone_battery&taxo%5B19%5D%5Bterm%5D=wqsftaxoall&taxo%5B20%5D%5Bname%5D=phones_other-features&taxo%5B21%5D%5Bname%5D=phone_price&taxo%5B21%5D%5Bterm%5D=wqsftaxoall&cmf%5B0%5D%5Bmetakey%5D=make&cmf%5B0%5D%5Bcompare%5D=1&cmf%5B0%5D%5Bvalue%5D=wqsfcmfall&skeyword=&wqsfsubmit=Search

The link is fine.

Try this :

if(isset($_GET['wqsfsubmit'])){
include(TEMPLATEPATH . '/search-phones.php');
}else{
include(TEMPLATEPATH . '/search.php');
}

If this failed again, then might be your search-phones.php problem?

I am really lost now. nothing gonna work. I have created even the basic search template and call it from my search.php. I think i am putting the above in wrong place. Please be specific exactly where i put this code. i added this just after :-
<?php if (have_posts()) : while (have_posts()) : the_post(); $postcount++;

which finally looks like

<div class="section">

                <?php _e( 'Search Results', 'made' ); ?>

            </div>        

        </div>

        <div class="ribbon-shadow-right">?</div>   

        <div class="section-arrow">?</div>

		<?php if (have_posts()) : while (have_posts()) : the_post(); $postcount++;
if(isset($_GET['wqsfsubmit'])){
include(TEMPLATEPATH . '/search-phones.php');
}else{
include(TEMPLATEPATH . '/search.php');
}

$thisPostType = get_post_type(); //get post type
			$thisReviewType = $oswcPostTypes->get_type_by_id($thisPostType); //get review type object
			$isreview=false;
			if($thisPostType!='post' && $thisPostType!='page' && $thisPostType!='attachment') $isreview=true; //set review variable
			if($isreview) {
                $icon = $thisReviewType->icon;
				$icon_light = $thisReviewType->icon_light;
				if($oswc_skin=="dark") $icon=$icon_light;
                $cat = $thisReviewType->name;
            } else {
                $cats = get_the_category();
                $cat = $cats[0]->cat_name;
            }
			//show rating?
			$rating_hide = get_post_meta($post->ID, "Hide Rating", $single = true);
			//check if this is a video post
			$isvideo=false;
			$video = get_post_meta($post->ID, "Video", $single = true);
			if($video!="") $isvideo=true;
			?>

Okay, another option.
On top of your search.php file (before the get_header();), put this conditional check.

<?php
$options = get_post_meta($_GET['formid'], 'awqsf-relbool', true);
if (isset($_GET['wqsfsubmit']) && $_GET['wqsfsubmit'] == $options[0]['button']) : get_template_part('search','custom'); return; endif; ?>

On the search-custom.php template (or whatever you call it, by referring get_template_part(‘search’,’custom’)), you create a whole new search result template, including the get_hearder and get_footer.