From memory headlights are around 5A so i would spec a 20A continuous diode each.
The cap has to be quite big, maybe supercap size. Thats not too much of a an issue. You can get them easy enough. Cost a bit through.
The issue is when the system first powers up and the caps are empty it's going to draw huge current (30A+) and may burn out the diodes. So maybe add a series resistor that limits inrush current under the diodes pulse current.
That's a good point about empty caps. I was already planning on having the relay
after the capacitor rather than before it, so that there's no current surge every time the headlights turn on, but when the battery is first hooked up to this it could definitely be an issue. Perhaps I can add a switch for the resistor, so it can just be disconnected easily once the capacitor is charged.
Your may get a better result just putting big caps at the amp though. I dunno
That's what I'm trying to avoid. Those things scare me, anything off-the-shelf for that is very sketchy and stupid expensive.