Template_redirect works, but headers aren’t sent when checking via cURL

I’m creating a 307 redirect to maintenance page for when my site goes through maintenance.

My PHP class is included in functions.php, and gets instantiated immediately.

In my __construct, I call:

add_action('template_redirect', [ $this, 'redirectToMaintenance' ] );

Then my redirectToMaintenance() method looks like this:

public function redirectToMaintenance() {

 $pageToLoad = get_the_permalink(123); // for test page ID

 header( "HTTP/1.1 307 Temporary Redirect" );
 header("Location: ". $pageToLoad );
 die();

}

This works perfectly, but if I try:

curl -iL https://example.com

No redirects are detected.

Same thing when I check via wheregoes.com.

I’ve tried redirecting with hooks other than "template_redirect" but they don’t seem to work well.

Any idea on what I could be doing wrong?

Thanks!