I will try it out on a Franklin Christoph that tends to dry out after weekend when I am back to office on Monday (I have yet to own a GVFC Intuition )
I personally own quite a few different Intuitions. I find that out of the ones I have, the only one that dries out is the one with the bigger nib which momentarily I forget the name of. My personal Intuition Platino is one of my favorite pens and I don't have any problems with the pen.
Using the GVFC inks are fine but they are on the drier side which might make the problem worse. If you want to make sure that the pen does not dry out, try a more lubricated Japanese ink like Iroshizuku or Sailor Jentle. Also go for the blue inks as their chemical makeup makes them less prone to drying out. I know because I have a retracting nib pen that for all intents and purposes functions like a pen with no cap. I found lubricated blue inks work best and don't dry out as quickly as inks of other colors, especially black and red.