Troy...those panels use a switchmode inverter power supply...converts 240V to 12VDC.
Most Switch modes operate at around 15-30Khz...I suspect this PSU is either radiating EMI noise or more than likely is sending unregulated noise in it's output 12V. More than likely...the latter...noise on the 12V rail.
If you move the PSU away from the EL panel (use/make a 12V extension lead)....does the interference reduce?
Or if as I suspect it's noise on the 12V rail...try a ferrite bead on the 12V PSU cord...as a RF filter..see
here or
here or
here. Or even another 12VDC source.