RV-12iS Idle RPM Fluctuation

What is your propeller type? On my CTLSi, i do experience the same due to the use of an eprop (very light prop) according to FD, this is normal.

It isn't normal and sounds like a fuel delivery issue. Props don't know a consistent and regular cycle. The prop shouldn't be affecting this. Does the fuel pressure or fuel flow change with this? 

Since the plane sounds new you may have collected some extra debris from Mfg to assembly and have some in the fuel filter. Does it change with one pump or the other or both running?

I've recently changed the fuel filter and the screen inside the fuel tank during the conditional.  I haven't really paid attention to this issue as I've either grown accustomed to it or been told it's normal.  

What is bothering is a drop in fuel pressure during high altitude climb, especially after a long climb with the throttle full open.  Retarding the throttle back to 5,200 RPM restores fuel pressure.

Do you have a Differential Fuel Pressure sender?   Or is your Fuel display properly configured?
What pressure are you displaying and how much is it varying?  Numbers, Please! 

This is a late reply, but the RPM fluctuations and the fuel pressure dropping seemed to have improved using 100 LL.