This is very easy to do
Easy Peeze.... These types of requests... are outside of the standard HumV's limited wiring needs, BUT your custom brake light setup will not break the bank and work the way you asked with a simple modified connection. Note: This write-up was design to NOT work in the military "Blackout" condition, which is a good thing, as I am following the military lighting protocols.
This is very easy to do.... NO need for any converters, switches or backwards thinking. Just a long piece of wire, say 14 gauge to route from the headlight switch and the 24 volts to instantly signal your intent to STOP when mashing the pedal. (check to be sure of LED voltage & or the bulb to be 24 Volts)
Here we GO... Remove the large connector, back of the headlight switch. Of all the wires, locate wire tag number 22A. You will need to tap into this lead. It is the common brake light circuit in the "STOP LIGHT or SerVice Drive" position.
Run the wire to the location of your ‘cyclops’ light and note this is the positive lead. You will need provide a ground to the other lamp lead. (some LED lighting may have a RED & Black wires making this even easier ???) Incandescent bulbs the socket ground, center pin positive) This statement is a bit wordy... but just want to clarify...CUZ I don't know what you got, CUZ
Total cost ??? A couple of bucks for the wire, a way to tap into the 22A lead, some time to route the wire front out around down over under to the back and a ground connection and the cyclops’ light. That's all you need and some time.
Some may have a better way.... Some.

The HumV and its single filament STOP & TURN design makes for IMO this the simplest, straightforward and cheap and done. Follow all good practice of routing wires, connections.
The “electrical” part by, CAMO
