I figured it out after reviewing the code reference for is_singular some more.
Here is the final code:
add_action( 'genesis_entry_footer', 'dr_prev_next_post_nav' );
function dr_prev_next_post_nav() {
genesis_markup( array(
'html5' => '<div %s>',
'xhtml' => '<div class="navigation">',
'context' => 'adjacent-entry-pagination',
) );
if ( is_singular( array( 'employees' ) ) ) {
echo '<div class="pagination-previous one-half first alignleft">';
previous_post_link( '%link', 'Previous Employee' );
echo '</div>';
echo '<div class="pagination-next one-half alignright">';
next_post_link( '%link', 'Next Employee' );
echo '</div>';
echo '</div>';
} elseif ( is_singular( array( 'work' ) ) ) {
echo '<div class="pagination-previous one-third first alignleft">';
if (strlen(get_previous_post()->post_title) > 0) {
previous_post_link( '%link', 'Previous Project', TRUE, '', 'work-type' );
} else {
echo ' ';
}
echo '</div>';
echo '<div class="one-third content-centered">';
echo '<button id="toggle-content" class="project-toggle">Project Description</button>';
echo '</div>';
echo '<div class="pagination-next one-third alignright">';
if (strlen(get_next_post()->post_title) > 0) {
next_post_link( '%link', 'Next Project', TRUE, '', 'work-type' );
} else {
echo ' ';
}
echo '</div>';
echo '</div>';
} elseif ( is_singular( 'post' )) {
echo '<div class="pagination-previous one-half first alignleft">';
previous_post_link( '%link', 'Previous Publicity Article' );
echo '</div>';
echo '<div class="pagination-next one-half alignright">';
next_post_link( '%link', 'Next Publicity Article' );
echo '</div>';
echo '</div>';
}
}