Linearization with Piezo Pro Inks

I re-read the Piezography Manual and I’m unsure what settings are needed for printing the 51 step target with PiezoPro inks.

When I print the 51 Step Target for linearization of the curve, does it matter what curve (cool, neutral or warm) I select for Shadows, midtones, and highlights? The manual shows printing the target with one curve for the Carbon inkset.

Do I need to individually linearize each of the three curves (warm, neutral and cool) applying each 100% to the shadows, midtowns, and highlights? IF so, will any combination of the three in shadows, mids, and highlights automatically remain linear?

I seemed to remember a conversation that the L Values of the warm and cools inks shades are not equal. If so, and I vary the blend of the two, will overall resulting tonal scale not be linear?