Are they the exact same brightness with or without the turn signal? Or does it get slightly brighter when you turn your signal on? I'm running into a similar issue with my '15 300R. I'm trying to install switchback halos as a part of my headlight retrofit but the way Honda did these turn signals is hard to work with.
I was able to measure the signal at the front turn signals, the dimmer "running light" mode is actually a PWM pulse with about 60% duty cycle, and the full brightness for the turn signal is a constant 12V. The dimmer PWM is still enough to trigger the switchback input of the halos, so they won't turn off of amber.
I've been trying to build a simple circuit to filter that PWM out so that only the constant 12V gets through, which sounds like what you need as well to make your mirror work. No luck so far though. I wonder how many other bikes are wired like this, maybe someone else has solved this already.
What mirrors did you get?