Is it possible to do this via TotalMix?

You could set up the mics as a stereo pair, a little further away, like a meter or so. Does might give a much more natural result. You can experiment with the distance and the mic placement.

What you want can be made with a side chain ducking gate. This is not possible in TotalMix, but you can do it in the post production.
https://www.youtube.com/watch?v=NcWd3HEqLKI

I/you do have gate/expander on my(your) TotalMix..

Thank you very much for participating and trying to clarify this for me, especially to Audio AG Support for confirming that this, unfortunately, isn't possible in TotalMix.

Please don't get me wrong, and I apologize in advance but in my OP I tried to avoid going into detail about my setup so that the main idea would come across more quickly—it worked. Now I got the answer, I’ll explain it in detail:

Since the RME gear is well-suited due to its neutrality and transparency—even for classical musicians, I opted for 2x DPA 4090s, which are also neutral, in an AB stereo configuration and connected directly to the UCX2 preamps exclusively for my saxophone sound.

For my voice—which is secondary in the project but essential for communicating concepts—I have other options, e.g., the Audio-Technica AT4080, which I also love for sax, connected to an external preamp and routed to the UCX2’s analog inputs 7/8. ... but the AT4080 isn’t neutral, and that’s the first reason I asked about the inverse/reverse gate in TotalMix. So far, I’ve been managing everything in TotalMix without a DAW or post-production. Excellent results.

But in addition, using the UCX2’s analog outputs 5/6 along with a Palmer PLI-05 and a Y-cable, I send the entire fully-mixed signal directly to the video camera, and I use the camera’s HDMI output to send video+audio directly to a Decklink Mini Recorder HD PCIe, recording on my PC without a memory card which saving time and hassle.

This method is perfect for me, and it’s true, without a DAW and using TotalMix there’s no latency ... it’s worth every penny!

The downside of this convenient and lightweight method is that I have to do everything in TotalMix because I only have one stereo audio track in DaVinci Resolve, where I can access all my plugins and the ASIO driver selecting the UCX2 as audio device. Here’s the second reason why I’m asking about a inverse/reverse gate in TotalMix.

I’m aware—and fortunate—that I have DURec, which I also use to save a copy of my audio sessions, but as I’ve already said, in terms of convenience for me, my method is unbeatable saving time in post-production.

@waedi, @kicksnarehat:
Yes, I considered a headset microphone and an ARC USB, but my goal is to avoid interacting with hardware during sessions, and with either of those, it would be unavoidable to cancel out the saxophone on the vocal microphone. Anyway, I really appreciate your ideas :)

@vinark:
As always, a very accurate shooter :)

@ramses:
Thank you for introducing me to Tomo Fujita. In my case—and without intending to compare myself to such an influential musician and teacher as he is—I need to manage two natural sound sources with different sound pressure levels, which means different gain settings for each. Using AutoSet, the DPA4090s (for sax) have been set to 28 dB. So, given the distance from the sound sources—with the saxophone right up against my body—my voice sounds distant and faint through the DPAs, lacking presence. I could fix this in post-production, but as I mentioned before, I’d like to avoid that.

@pajautus:
That's right—for non-experts and non-pros like me, TotalMix's presets are a godsend!

@RME:
I realize that my request might seem rude coming from someone who wants to avoid post-production, but if possible—if you think it’s appropriate and your time allows—please provide a inverse/reverse gate preset in TotalMix. In any case, congratulations on your amazing development!