7.3 * 1.414 0-peak for the regulator makes it about 12 V, sort of, if it were filtered and rectified.
In any event, what I am advocating is to:
1) Change the resistor(s) is a stock LED lamp to lower the voltage.
2) Add a current regulator if necessary
3) still carry a spare
4) You might have to change the socket
5) The bike, I think, would have to run if the bulb is removed.
Caveots: Accessibility of the resistors. I have in my possession a #194 replacement lamp that works on 12V when installed din the proper direction. I KNOW I could change that voltage to anything by changing those resistors. To make it operate on an AC voltage would take a bit more work.
What they actually could have done is to use a lamp as a current dependent resistor in the ignition coil circuit. In that case, it is a real active device and a regulator would be the best choice, but I still doubt it. Getting it small would take some effort.
Just being suggestive, a box such as
https://www.polycase.com/wa-series might be able to be used. I had an electronic ignition which did have a heatsink and a single TO-3 transistor exposed, so I doubt that is much of an issue to have it exposed. There were plastic covers available for the transistors. So, it would take some effort. Making a PCB would make it more reliable as well.
My initial thought was to build it into the tail lens, but I don't think that will happen.
So, I still like the idea of making a LED replacement work, Just not sure how to go about it without more info:
1) bulb type #
2) pictures of the tail light assembly
Worst comes to wose, you might have to "home grow" your own socket. One connector that comes to mid is this
https://uk.farnell.com/molex/38330-0503/plug-socket-connector-female-12pos/dp/1164039 one.