update meta field value after

You are not retrieving the saved value for $model.

$model = get_post_meta( $post_id, 'auction_model', true );

And you should be sanitizing the values upon retrieval, or at least before echoing them:

<?php echo sanitize_text_field( $model ); ?>

You could also check for the value before calling update_post_meta() upon form submission, unless you intended to run that every time this page is loaded. If nothing else, you can at least check if $_POST has a value:

if ( isset( $_POST['auction_model'] && ! empty( $_POST['auction_model'] ) ) {
    update_post_meta( $post_id, 'auction_model', sanitize_text_field( $_POST['auction_model'] ) );
}

You can also then delete meta if the form field is empty:

else { 
     delete_post_meta( $post_id, 'auction_model' );
}

You can read more on sanitizing and validating user input here.

And more on the three *_post_meta() functions mentioned above here:

update_post_meta()

delete_post_meta()

get_post_meta()