It is possible to connect to 3rd party telephone hybrids (POTS/ PSTN/ ISDN/ VOIP/ SIP) to your Eclipse matrix and dial out using DTMF tones from the matrix MVX-A16 port.
Note
Detailed Solution
To produce a DTMF signal from an MVX-A16 card set the port function to a TEL-14, and then latch a key to the port and dial from a panel or use a speed dial. There's no need to connect a TEL-14, it's just a handy way to make the system behave as you need.
The trick is to make the Eclipse believe that something is connected. To do this turn Hardware Detect (Cards and Ports > Advanced Settings) OFF.
If you don't have this option in the ECS / EHX version you're using:
From the matrix MVX port . Make a cable with an RJ45 connector that loops back pins 1 to 7, 2 to 8 but leaves the other pins alone. I find the EZRJ connectors (http://ezrj45.com/ezrj45plugs.php?gclid=CNW35ob-vrkCFSlo7AodxhUAqg) make this easier to achieve.
The other RJ45 pins 3+6 and 4+5 are the balanced 4wire audio lines to/ from the matrix.
Once your MVX port is connected to the third-party hybrid you should be able to make and receive calls as you would with the TEL-14.