I think you already understand that the EN is an input and the board already pre-wires it with a \$270\:\textrm{k}\Omega\$ pull-up to VIN (via a protection circuit.) I'm going to assume you aren't doing anything to drive the EN input, since you haven't mentioned doing that. This just means that when VIN of \$12\:\textrm{V}\$ is connected up, the EN will automatically enable the output. That probably isn't a problem for you.
Given that fact, you just want to observe the PG output, which is an open-drain/open-collector style of output, and use that to control two different LEDs. One that is green when PG isn't actively trying to sink current and one that is red when PG is actively trying to sink current.
If the power isn't good for some reason and you want the red LED turned on, then the only power you can rely upon is the \$12\:\textrm{V}\$ input source. You have to assume that the output of the regulator "isn't good" and so you should NOT be using it to power the red LED.
But even assuming the PG output could directly handle the required current for a red LED (low current, high efficiency, for example) and then attempting to use the PG output to directly sink current required for it may also lead to another consideration (worry.) It may be possible that the PG output can't tolerate a full \$12\:\textrm{V}\$.
It's hard to be absolutely sure about that, since Pololu doesn't tell us which device they are using and their pictures appear to have had the numbers ground off or erased in some way. This means you may have to make an assumption, which could damage the input if you are wrong. But unless the buck converter IC designers went out of their way, it's likely that the PG output can tolerate \$12\:\textrm{V}\$. I just wanted to point out that this is an assumption I wish I didn't have to make.
Yet another assumption returns us to the amount of current sinking capability for PG. It takes a big internal transistor to sink enough current for a \$20\:\textrm{mA}\$ LED. I'd be worried about using it to sink \$20\:\textrm{mA}\$, especially since the only words the web site uses regarding the PG output is to suggest a pull-up resistor (which might imply that an LED won't work well there.) So if you can select one of the low current, high efficiency \$2\:\textrm{mA}\$ LEDs, then I think I might go that approach and plan on the idea that the PG output can handle the current. (It's not that much of a risk because these LEDs are quite visible, even with just \$1\:\textrm{mA}\$.)
If the power is good, and PG isn't attempting to sink current, then you have two options for the green LED. You could still source current for the green LED from the \$12\:\textrm{V}\$ input source OR you could source that current from the \$5\:\textrm{V}\$ output (which should be close to \$5\:\textrm{V}\$ if PG is indicating "good".)
I may not decide to use the \$5\:\textrm{V}\$, but instead rely entirely on the \$12\:\textrm{V}\$ input source for both purposes. In some ways, this choice is arguable, though. (One might read datasheets and find that the \$5\:\textrm{V}\$ requires a minimum load and argue using the green LED as that load, for example.) But I don't find those persuasive and I'd make the choice to use the \$12\:\textrm{V}\$ input source for both LEDs. If the output needs a minimum load, I'd provide for that in a managed way, separately. I'm not going to make all the arguments here, though. It would distract things way too much.
Those are my thoughts before embarking on making any suggestions. To keep the circuit simple, try and buy low current, high efficiency red and green LEDs. In this case, just adding one NPN BJT and two resistors is enough to handle both LED cases. Otherwise, if you have to use the higher current (normal) LEDs as indicators, then I'd go with a more complex circuit (shown at the end, below.)
(The risks in either case shown below are that PG can't even sink \$1-2\:\textrm{mA}\$ and/or that it cannot tolerate \$12\:\textrm{V}\$ impressed on it when the red LED is OFF. Both risks I consider to be relatively small.)
So, let's assume that you will be using low current, high efficiency LEDs and that we can reasonably assume that the PG output can sink the LED current of \$2\:\textrm{mA}\$. So, with that in mind, here is the schematic I might try which covers both LED drive needs from a single BJT:

simulate this circuit – Schematic created using CircuitLab
If, on the other hand, you can't use low current, high efficiency LEDs for this purpose, then I'd assume that the PG output cannot directly handle the load. So I'd then try this:

simulate this circuit
But it's not quite as simple as you wanted. I'm sorry about that.