Well, first off I'd never cut into the car harness to do such a thing, but that might just be me! Many LED marker bulbs come with a short extension cable, so cutting into this would be my advice.
The exact value of the capacitor will depend a little on the exact characteristics of the LEDs you have, but a rough calculation would indicate that if the pulse is about 100 mili seconds then you'd need a capacitor of around 2,200μF (micro Farads). This may be a little on the small side, but you should not go too big as it will cause a large current draw when you turn the lights on, if you use a much larger capacitor you may also need a small resistor (low resistance, but quite high power to be safe) to prevent a very large surge. A capacitor of that sort of size will mean using an Electrolytic capacitor, so you need to get the polarity right (they are more like a small battery) and make sure that it has at least a 25V rating, common values are usually 16V, 35V or 63V.
I've not done this on mine, but I do plan to do it in the near future, so if you hold fire a bit I'll be able to give exact values and a DIY. But if you do it first let me know what you used!