Always show Next and Previous button in wp_link_pages ?

I’ve just faced the same issue and here is my solution. I’m using globals to get current page and total page count:

/* first i'm looking into $multipage global to check 
if the post actually has pages */
global $multipage;

if ( $multipage === 1 ) {
    global $page; // this is current page number
    global $numpages; // this is total page count

    // display disabled left arrow on page 1
    if ( 1 === $page ) :
    ?>
        <span class="pagination__arrow pagination__arrow--prev pagination__arrow--disabled">< Previous</span>
        <span class="pagination__separator"> | </span>
    <?php 
    endif;

    // standard wp pagination
    wp_link_pages( [
        'next_or_number'   => 'next',
        'before'           => '',
        'previouspagelink' => '<span class="pagination__arrow pagination__arrow--prev">< Previous</span>',
        'nextpagelink'     => '<span class="pagination__arrow pagination__arrow--next">Next ></span>',
        'separator'        => '<span class="pagination__separator">|</span>',
    ] );

    // display disabled right arrow on last page
    if ( $page === $numpages ) :
    ?>
        <span class="pagination__separator"> | </span>
        <span class="pagination__arrow pagination__arrow--next pagination__arrow--disabled">Next ></span>
    <?php
    endif;

}