In the case of a VFD check filament voltage of course, however most of the time this is a symptom of bad small (22-100µF / 50-100V) electrolytics on the cathode-anode drive voltage (usually 20-30V).
Looking at the TS-870S service manual the display is an LCD with CCFL backlight (or electroluminescent sheet) in that case I'd suspect a weak CCFL, but it is also worth checking capacitors around the inverter.