According to Moss, even with an electronic flasher, some cars will need ballasts
Do I need ballasts with my LED turn signals?
Not all Classic British Cars need ballasts, but if you own any of the vehicles in this list, then yes, you will need ballasts in order for your LED turn signals to function properly:
• TR250 All
• TR6 69-76
• Austin Healey BN1-BJ8
• Sprite/Midget 1972-on
• Spitfire 1500 To FM 6000
My 76 midget is in this group.
It has to wit the wiring of the signals. When you turn on the signal for one side a small amount of current makes it to the other side. With normal bulbs it isn't enough to make the opposite side light. That isn't the case with LEDs. Although it is a small amount of power it is still enough to light an LED so when you turn your signal both sides flash. The ballast is needed to bleed of the stray power do the opposet side won't light up.
This is a video from Moss that explains the situation however it doesn't say if one ballest per side is enough.