It seems quite probable that the “Aux” input on the Beachtek DXA-2T is line-level and not mic-level. Alas, Beachtek seems to be following in the modern tradition of “dumbing-down” documentation to the point where it isn’t useful any more, so it is not clear exactly how the “Aux” input is designed. Yes, I realize that I am tilting at windmills and there is no hope of reversing this informational entropy.
But in any case, the Aux input will NOT work with the Sony HXR-MC50 microphone. While that microphone is NOT “stereo”, the connector is wired to send the mono signal to both the left and right channels of the camcorder. And it requires “plug-in power” from the camcorder. This power is eliminated by the Beachtek box and not passed through to any of the input connectors.
While the Beachtek box is a handy gadget, it is NOT a suitable solution for what you are trying to do. The microphone on the HXR-MC50 is a specialized design and operates properly only when plugged directly into a consumer mini-jack mic input. I have not seen ANY commercial equipment that allows use of both conventional XLR microphones AND 3.5mm mini-phone “plug-in power” microphones.
I have an HXR-MC50 and it is a very nice little camera, but I would have to build a custom version of the Beachtek box to allow that kind of “mixed-mode” use. I am actually considering doing that because I have a similar need.
Or the Beachtek box could possibly be modified to allow such use, but, of course that would void the warranty.
The Rode mic may work, but not plugged into the “Aux” input, you would need to plug it into an XLR mic-level input with an appropriate adapter.