It is a LED assembly and it runs, along with the fourway flashers, a bit differently than the tail lights...and that is all I know, lol.
I'm researching another aspect back there and it was an auto-electric guru who was explaining all that to me but its Chinese Algebra insofar as I'm concerned.
Anyway, my long winded way of saying I doubt it is the light (bulb) itself. Somewhere in that circuit which is independent of the stop lamps will be your problem.
Maybe the dealer or a mechanic you know will print out a wiring diagram for you?
Mine came out of the Mitchell Repair Information Co. LLC. online data bank which is a subscription only thing for licensed mechanics and shops.
Anyway, from the TIPM (Totally Integrated Power Module) on the left rear of the engine compartment it is a Dark Green with White stripe wire that runs through the driver side door sill in the main body harness where it splits, part going to the Stop Lamp Switch under the left (driver's) side of the dash and part going to the High Mount Stop light. In both cases the wire remains Dark Green/White stripe.
The ground from the High Mount Stop Light is Black with a Light Blue stripe and it terminates at the left, rear quarter panel, under the trim.
BUT....here is where it gets scary...That Dark Green with White stripe wire carries on to a Stop Lamp Switch Output that then enters what are called "computer data lines system" and goes back to the CANBUS.
None of the other lamps back there do this, not the license plate ones nor the tail lights.
Anyway, if you pull the trim panels back there you will see way too many wires running into or out of that High Mount Stop Light...too many for me, for sure.
But it is Dark Green with White Stripe...so get a multi-meter and someone (maybe you, certainly not me) who knows how to use it and start looking.
I'd start by looking for corrosion in the wiring loom under the drivers side carpeting...that particular area seems to pop up often.