I was having a similar issue with this, I fond a solution that isn’t exactly the most elegant work-around, but it does the job.
Firstly, make sure your body tag reads:
<body <?php body_class(); ?>>
This’ll add a class to your body that will be unique to your custom post type. Next thing to do is go to your custom menu, make sure CSS Classes is turned on under Screen options, then give your custom link a class. You can then target it in CSS so it gets highlighted when under a particular body tag.
I realise this probably isn’t too useful for you 4 months on, but I thought I’d share it cos I went on a hunt for this info myself and A post explaining how to do it would’ve been useful!
