The issue is somewhere in the circuit for your front L (or the front R for @
Aggrotech). Either the bulb is bad (you said you eliminated that) or there is a loose connection. Since that one is not working, there is not enough load on the circuit to operate the thermal flasher which is why the rear stays on but does not flash.
As you said, try a known good bulb from the other side and see it that does it. If not, pull the fairing and check all of the connections between the bulb and the fuses. If you have a meter, the job is a lot easier. If you don't, go buy one, even a cheap analog one for like $10 will work. They are pretty easy to operate, way easier than Calculus.