There is some math involved with selecting the right transistor, but since I'm not an engineer and I personally hate math, I just leave all that alone, and find the best solution through educated guessing and trial and error.
I have some TIP105 (beefy) PNP transistors on order for another project, they'll be here in a week, I can breadboard it for you at that time... I'm kinda curious to see how it works myself.
Here is a schematic of my idea:

I was going to suggest some values for R1 and R2, however, I can't find anything good that will work for your 3 watt LED, at 700ma you are looking at 875 mw to be dissipated by the resistor, let alone 1400mAa, that puts you past the recommended safe range of a 1 watt resistor ... so you get into weird beasts like wirewound sand or you have to double up your resistors (that would mean four resistors total)
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Hang on! business major trying to do engineering, I hope Rob checks my math

Ok, so, for "running light mode" and "brake light mode", you want R1 and R2 to be the same, keeps math easy that way
For 700ma as the running lights:
1.25 / If = R is 1.25 / 0.7 = 1.8 ohms
closest easy match: two one watt 3.9 ohm resistors wired in parallel:
R
T = 1 / (1 / R
1 + 1 / R
2 / 1)
R
T = 1 / ( 1 / 3.9 + 1 / 3.9) = 1.95 ohms, and the current sent out is
I
F = V
ADJ / R
SET = 1.25 / 1.95 = 0.64 Amps which means the resistors will have to 'burn off'
P = I * V = 0.64 * 1.25 = 0.800 watts = 800 mW
Now for braking mode, which is R2, you want the full 1400 mA:
1.25 / 1.4 = 0.89 ohms
using the same resistor(s) you used for R1 again as R2 you have:
R
T = 1 ( 1 / 1.95 + 1 / 1.95) = 0.975 ohms, which yields output current of
I
F = V
ADJ / R
SET = 1.25 / 0.98 = 1.28 Amps which means the resistors will have to 'burn off'
P = I * V = 1.28 * 1.25 = 1.6 watts ... but 1600 / 4 = 400 mW each, so four 1 watt resistors should be fine.
As for R3, I'm not sure enough on how to calculate that, it needs to be based on the amount of current needed to be switched and the amplification factor of the given transistor (QFE) ... when you find a PNP transistor that can handle at least 3 amps, let us know what it is and I or someone else can help you figure out the value of R3