Pardon my not taking the time to research this in any detail... and you'll likely answer this efficiently. I did discuss the question briefly with a colleague and neither of us had a nice response for a student question. A student asked about neutrons.
I recognize that a neutron has a non-zero magnetic moment, that it is a collection of quarks with a total electric charge of zero. Here's the student question: If a neutron were made to move, would its electromagnetic nature result in EM wave propagation?
My first answer is no, but there is that magnetic moment and the substructure of the neutron. A cursory glance with Google led to one or two hits where people implied it might emit.
I thank you in advance for any response. Have a safe and healthy day!