LED systems come in basically two or three types
One type starts with a series resistor, and then the LED and that's all folks. This type, you put two of them in series, and it should work as you hope it will.
Some have voltage regulators, ahead of the series resistor, This one may well work on 24 volts without any mod (However I do not recommend it)
Some have a CURRENT limitere ahead of the led.. Same as the voltage regulated ones,,, And these should work in series as well (All 3 kinds should).
THe key is, as someone said up above, to keep the two assemblies the same.
Cause if one takes a bit more current, the other won't last long.
I have put LED's in series more than once.
NOTE: If you see a difference in the two LED's in the pair.. Try putting a resistor across them. say about 1,000 ohms. (That will cause 12mA to flow through the resistors) if it works, up it to 10,000 ohms (1.2mA) Like this.
Resistor-|--Resistor
--LED---=|==LED--
This is a fairly old trick, but it still works.
