Ha, bet you thought I had forgotten this
I just needed to do some tests "in the real world" because doing it using maths wouldn't work with the way these LED strips work.
So, after eventually finding enough bits of LED strips to make up enough to get to the 1 Amp figure requested I did some tests, with interesting results.
Because of the way LEDs work, they do not dim 50% when 50% of the voltage is applied.
My tests showed that from full brightness to almost out completely was from 12.6 Volts (obviously) to 5 Volts.
However, In my tests, the current drops off
very rapidly as the voltage is decreased. It was
very non linear (as LEDs are "semi conductors"). This means one cannot use a simple (wirewound, ~15W) potentiometer.
E D I T = reading back over my results below, if I had a 15W 500Ω pot, I would have tried it

Looking again at the results, i think it might be OK.
Also, as the voltage (and therefore the current) drops below about 8 Volts, the LEDs stop being white, the red LEDs in the strip obviously require less voltage to keep going, so as you go below 8 Volts the LEDs become redder and redder. This might be considered a quite nice feature.
By the way, I am assuming here we
are talking about the tri-colour versions of the strips?
So, what is the answer. Well, one cannot use one of the £6.70 DC adjustable voltage regulators available on ebay because they drop 3 Volts, meaning that on "full" with 12.6 Volts going in, they would only chuck out 8.6 Volts = no good. What one could do is arrange a multi position switch, just like the one that controls the three speeds on your heater blower. Feed it with 12 Volts, then, on the three output legs, solder on resistors. Or, you could use a rotary switch with more than three terminals, like these :-
http://www.ebay.co.uk/itm/Rotary-Switch ... 1Jf61Oa1OQ" onclick="window.open(this.href);return false;
http://www.ebay.co.uk/itm/2P6W-2-Pole-6 ... SwKtlWrRel" onclick="window.open(this.href);return false;
http://www.ebay.co.uk/itm/Rotary-Switch ... SwY45URh1i" onclick="window.open(this.href);return false;
And get more control.
Resistor values =
470Ω = very dim red @ less than 1mA !!
220Ω = dull red @ 1mA
100Ω = bright red @ 4mA
33Ω = almost pure white @ .15A (a 1Watt resistor would be needed here = pennies still)
15Ω = not quite full brightness @ .25A (a 2Watt resistor would be needed here = pennies still)
And of course one connection to give the full 12.6 Volts from the battery. (1 whole Amp for my strip totalling 48 SMD LEDs)
Or, you could just have a three position ordinary switch = off / full power / via a 220Ω resistor for a medium red output. This would be cheap and easy option (about £2 would cover it).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Slight aside = I bet Ralph and some other electronics nerds will be a bit surprised at those very low current figures the LEDs draw whilst still emitting useful amounts of light. Turn um down lads and save your leisure batteries power for the Propex
