I don't believe you have an EMI issue from any external source, however it is remotely possible that there is an intermittent EMI source radiating from the control housing and the coil is picking it up.
If that were the case, there would be a measurable signal emanating from the control housing. In order to test for this, a wide-band probe (it's a multi-frequency detector) and a spectrum analyzer or EMI receiver would be required.
Before going to that amount of effort and expense, I would disconnect the coil from the control housing and carefully check if any of the pins show corrosion. If there is none, then I would proceed with trying an alternative coil.
Also, while this next suggestion might sound a bit odd, it's worth a try.
Cut a piece of aluminum foil about twice the size of the control housing, including an extra inch or so on each side.
Fold it in half, and wrap/form the foil around the control housing top, sides, bottom and back. Use black electrical tape and wrap all metal parts of the coil connector on the back, and then form the foil around the cable/connector. Do not allow the foil to have direct contact with bare metal on the coil connector in back.
Charge it up and take it out in the field for a day and see how it performs. Let me know if there are any changes to the chattering, or if it shows up at all.