Try wp_page_menu('include=' . $IDvariable); and ensure that your variable is a simple string – not an array.
The problem with your code is that you can’t use variables inside single quotes, so the value is treated literally.
Esmi’s suggested code above will fix that by concatenating the string, alternatively you can also use double quotes so the variable is interpreted.
Eg.
wp_page_menu("include=$IDvariable");
The variable is indeed a simple string made with implode(); from an array.
Both solutions work.
Thanks! Really appreciate it.