6v 12v switching, converting?

I have 2 bikes, a moped and a street/trail bike that are 6v systems.

I need to run 12v for my aftermarket speedometer/tach but want it to come on when the bike is started or power turned on.

It draws little power as do my aftermarket LED tail/brake and turn lights.   (The LEDs are running on the 6v system generator through diode bridge to make DC, right now just fine, might be brighter when I install my new batt, 6v)

Can I carry a small 12v sealed cell(I already do for speedo) but use my stock 6v AC or DC from Diode bridge/charging output, to trigger a common SPDT relay to pass through the 12v DC to my new speedo & lights?   In same sense if I were to change to 12V headlight, use output from my 6v stock switch to pass 12v to headlight?

In your opinion can I get "any" charge to the 12v batt from the 6v system?  I figure if I use a stock 6v system with the batt, Then use a diode to a 12v batt parallel to the 6v, this way the 12v won't feed back to the stator/rectifire.    This batt runs the extras for a week as is without a charge and is only a 3AH 20/H 12v, so even if I get extra week or even half week I gain.

Possibly something like this:

http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail?name=296-3226-5-ND

there are voltage doubler circuits that can easily be made. I am not sure if this will work without being isolated somehow from the 6 volt demands. basically if you can tap the ac voltage before the rectifier, input it to the doubler circuit, the voltage will be close to double from the output, delivering half the current. from reading posts in the past, hotwater wizard sounds like a good man to ask.