Connecting to a 2nd DB gives me no results when querying

This is a variable scope, an pure PHP, problem at heart.

I didn’t close it because I am assuming that mistake is in turn due to a misunderstanding of the init hook, or hooks in general perhaps, which is WordPress specific.

1. In PHP, a global must be declared global before the first time
   it is used.
2. The init hook fires very early in page load, long before your
   page.php executes
3. Your $newdb variable is not declared global until page.php
4. Thus, the variable is declared global after it has been used in
   the init action, and thus too late.

PHP executes line by line in sequence. Order matters. The order that hooks fire determines the order of the code in any of the “attached” functions.

To fix this, declare your variable global in the callback to the init action hook.

add_action('init','my_new_db');
function my_new_db(){
  global $newdb;
  $newdb = new wpdb( 'test', 'test',  'test',  'localhost');
  $newdb->show_errors();
}

You will still need global $newdb; in your page.php file to access the global you’ve created. Don’t remove that.