Or you could use a more sophisticated circuit and have one of the color changing LEDs (red for lo/no charge or charging, and green for full).
Way better is to keep these LEDs separated: With quick look, you may misinterpret the color, but you will see pretty well, if there is just one or two LED's ON, even when you would be color blind...
And it becomes a standard (dunno how official, but most emergency fixtures behave that way):
Control light ON => Input charging mains connected, fixture working (but does not mean the battery being really charged)
Only main lamp ON, control OFF => Input power missing
Both main and control OFF => fixture faulty or main power OFF too long (as inspections are usually done when the power is running, it likely means input power fault)
Control flashing (only in some fixtures) => Battery running flat; if the main lamp is OFF, it was shut down by the undervoltage protection
Except the flashing (flat battery) signal, all is ensured by just the LED (or the incandescent) in the charging path and normal lamp control (LED is ON only when the charger is running and the battery is connected, what means mainly all fuses are OK, wiring gets power, batteries are not dried out so open circuit,...).