SearchWP Live Ajax Search results template to output a custom Source (Users in this case) https://searchwp.com/documentation/knowledge-base/custom-source-results-live-search/

search-results.php

<?php
// Execute a search using our supplemental SearchWP Engine.
$search_query = isset( $_REQUEST['s'] ) ? sanitize_text_field( $_REQUEST['s'] ) : null;

$search_results = [];
if ( ! empty( $search_query ) && class_exists( '\\SearchWP\\Query' ) ) {
	$searchwp_query = new \SearchWP\Query( $search_query, [
		'engine' => 'supplemental', // The Engine name.
		'fields' => 'all',          // Load proper native objects of each result.
	] );

	$search_results = $searchwp_query->get_results();
}
?>

<?php if ( ! empty( $search_query ) && ! empty( $search_results ) ) : ?>
	<?php foreach ( $search_results as $search_result ) : ?>
		<?php
		switch( get_class( $search_result ) ) {
			case 'WP_Post':
				?>
				<div class="searchwp-live-search-result" role="option" id="" aria-selected="false">
					<p><a href="<?php echo esc_url( get_permalink( $search_result->ID ) ); ?>">
						<?php echo get_the_title( $search_result->ID ); ?> &raquo;
					</a></p>
				</div>
				<?php
			break;

			case 'WP_User':
				?>
				<div class="searchwp-live-search-result" role="option" id="" aria-selected="false">
					<p><a href="<?php echo get_author_posts_url( $search_result->data->ID ); ?>">
						<?php echo esc_html( $search_result->data->display_name ); ?> &raquo;
					</a></p>
				</div>
				<?php
			break;
		}
		?>
	<?php endforeach; ?>
<?php else : ?>
	<p class="searchwp-live-search-no-results" role="option">
		<em><?php esc_html_e( 'No results found.', 'swplas' ); ?></em>
	</p>
<?php endif; ?>