This is not something that can be done in Thetis or via Thetis. Thetis has no way to tell Voicemeeter what is happening, and Voicemeeter is where the switching or muting needs to happen.
However, Voicemeeter does have a way to do this automatically. It has a powerful scripting and macro add-on which is installed with Voicemeeter, i.e. it should already be there for you. You define a macro button to "duck" (that's the industry term) the mic input when there is transmit audio coming on the virtual input from JTDX (or whatever). There is an example on Page 51 of the
Voicemeeter user manual (and no doubt some Youtube videos as well).
No need to duck in the opposite direction, JTDX should be very quiet when using the mic. In the example they use the "fadeto" scripting command, but I'd use the "gain" command because you want it to be instant, and you'd lower the gain to the minimum possible during the ducking period. I'm not sure it's possible to use mute, but you might experiment with that.
Before you start asking for help I should write that I've never done this myself
But it should work.
Note that it is not terribly difficult to use the VB Macro buttons to send CAT commands to Thetis, which is pretty cool. I've tested this and it works, in fact Vincent specifically added a way to "escape" the ";" character for me to allow this to work. So if you want to get crazy you can write VB Macro buttons to make Thetis do all sorts of things (and Voicemeeter, too).
Additional note for budding programmers: someone could write some Python (or whatever) to query Thetis via CAT and send messages to the VB Macro facility to make things happen that way as well.