My first thought would be a fault inside one of the taps. Turn the 12v off and disconnect the feed to/from each one in turn by accessing the connector blocks in the cupboards beneath the sinks. Hopefully you should then find out which is at fault. I believe if you are clever you can take the taps apart and replace the switch inside and I'm sure somebody posted on doing this fix. If you cannot fix it then a replacement is expensive at probably £120 as it is a hot/cold mixer. I think Brownhills the Hymer Motorhome dealer may stock them, but I would shop around as you may be lucky to pick something up on e-bay.

Colin