A more difficult solution, but perhaps more cool:
Attach the engine as a seperate PCO which has its own hitpoints (representing the fuel) etc. Of course you'd need to somehow make the fuel capacity visible...perhaps make a small bar-like object with a fuel level indicator, position it so it's in the viewport of the pilot...Then you could have it show the different fuelstates by changing the textures according to its hitpoint level. BF doesn't support that dynamically, but you can workaround by using armoreffects. Attach the aforementioned death bubble (see W2Ks post) to slowly reduce the engines' HP. This would have the big advantage that you could "simulate" fuel shutdown by using "critical damage (which stops the engine)" without actually destroying the engine (Example: The engine has 1000HP, critical damage is set to 500 and HPlostwhilecritical is set to 0. This would mean when the engine hits critical, it stops getting further damage and still would have plenty of reserves so it doesn't get killed by "environmental" factores either (rockets, tanks, artillery)). This would mean if you managed to land an outoffuel-vehicle somehow and then repair it by wrench, vehicle or helipad your heli would be good to go again. And even your fuel level indicator would "rise" again
.You could further enhance that by allowing only specific kits or vehicles (fuel truck!) to "refuel" the engine PCO by giving it a unique material...
I'm pretty sure my idea would work with some workarounds, but it's hell a lot of work and definetly requires good modding experience. Would be a pretty unique mod feature however...