Your (+) terminal is actually (R) and your (-) terminal is actually C. You missed W which is usually heat. Here is typical thermostat wiring:
https://wiki.xtronics.com/index.php/Thermostat_signals_and_wiring
So, it looks like two-stage cooling and no heat or is AUX a strip heater?
Thermostats of yesteryear didn't bring the common terminal to the stat. You will need this.
Fortunately, your request is easy:
It just consists of an LED, A resistor and a diode (e.g. 1n4002). LED Vd is usually about 2.1 V, and usually you need abut 10 mA of current. A resistor sized to be about (24-2.1-0.6)/If. If typically is 10e-3 or 20E-3 Amps. 10and 20 mA respectively. The power rating of the resistor should be checked against (I^2)/R or the current in amps squared divided by the resistor. The resistor has to have a rating rater than the calculated power. e.g. 1/2 W resistor.
Knowing the LED specs, If, Vd, and Ipeak we can possible get the brightness higher.
So it's just a LED, a resistor and a diode in series and you pick the order. Only the polarity of the LED and the diode polarity matters. Make the arrow of the symbol face the same way.
One end of the simple circuit connects to (C) and the other to the specific terminals.
Depending on your construction technique, the circuit could be messy or easy.
An easy construction technique, but more expensive, is to use LEDs that are 12 V or 5V and have pigtailed leads on them. If you connectorize the wires, you can attach everything to a perf board with say depluggable terminals for the connection to the system. Modifying the resistor value using these LEDS may not be straightforward.
You can use other mounting clips for the LEDs or get ones that mount integrally on the panel. You can also connectorize this and make the connections to the leads directly.
I recently purchased a couple of IP67 rated LED's. Basically rain proof.
Another construction technique might use a SIP header, so you just lug the SIP header into all of the mounted LED's. That might be the easiest.
I'll reccomend the Metal Oxide type of resistor.