I have MX-65 and I terminated MPLS link on LAN Port (My MPLS doesn't have internet), I configured the device via dashboard by connecting the device on Internet and tested my MPLS network and found perfect, after testing I removed Internet cable and only kept MX with MPLS link but after sometime My MPLS also stopped working.
We tried to deploy a similar solution. The MPLS network needs to provide a path to the Internet. If it doesn't the MX will not check in to the dashboard and you won't be able to manage it.
What are you using your MX for?
From your description, it seems your "MPLS" is plugged in to a LAN port and nothing else is plugged in.
Where is the traffic supposed to go?
We programmed the dashboard with all appropriate IPs for the LAN interfaces. We then plugged the MX to an Internet connection to download the config. Then the MX was put on the MPLS network & we statically configured (from the setup page) the MPLS IP address. That didn't work. I called support & it was determined a router needed to be installed between the MX & MPLS.
The customer didn't want additional devices so we pulled the plug... so to speak 😉
If you want to use it just as router that want work because the MX need to be able to communicate with the Meraki server to verify your network. It's like not renewing the licence. Those equipment need to validate the licence also.