I'll get to answering what you asked in a moment, but first I must ask you why you are building your own. What is it you are out to achieve that you can't with a COTS unit? I'm not trying to imply that you shouldn't do it, as there are many good answers to my question. Just make sure you've thought about it before proceeding.
You probably need a resistor in series with the red LED. Look at the data sheet for the LED to see the maximum current it may draw at 12 volts and compare that to the guaranteed no-fire current of the igniter. (I have the no-fire current somewhere, but not with me.) Odds are, the LED current is enough, or nearly enough to risk firing the igniter. I would keep the continuity test current no greater than half of the no-fire current; that may be more cautious than necessary, but certainly don't let it exceed 75%. If it does then you need a current limiting resistor.
On the other hand, you might find that, with a low enough current to be safe, your LED barely lights up. If that's the case then you need a lower power LED.
Finally, if I were you, I'd reverse the LED colors. As it is, you light up green as soon as the power is on and red to indicate continuity. I'd prefer red, a warning, any time the system is on and green, a GO confirmation, when continuity is established. But more important than that, if you've got two lights then you should have clear, obvious labels stating what each light means. And if you have labels then the colors are not so important.