Alcohol inks

I would not suggest using them. Since the binder in these inks is alcohol soluble, I am guessing that the binder would precipitate when added to your egg/water mixture. I always cringe when a colorant is described as “tangerine” or “Sangria”, etc. with no pigment or chemical name attached. This does not mean that the product is poor but there is no way for me to judge its applicability. I also do not like that most of them are colored by dyes rather than pigments. Another think that I would add is that organic colorants, especially dyes are often prone to bleeding up through superimposed layers. This may not be a problem with these materials.

​​​​Hi,
The Material Safety Data Sheet for Jacquard’s Pinata Inks list ingredients as “Ethanol, Propoxyethanol [solvents] Modified Polymers/Binders, Colored Pigments”.  It says the formulation is proprietary, so not sure if we can know the polymer.  I sent an email to their tech staff asking about the binder, and if the inks are “dye-based”, as noted in the marketing, or “pigment-based” as the MSDS says.  I’ve previously found the labeling of this company to be unclear (specifically for their wax medium, Dorland), and agree with Brian that one should be cautious with companies more interested in enticing names than clear information.  
I don’t believe egg tempera adheres well to synthetic polymers (a.k.a. plastic) unless the material is very high PVC, and even then it can be questionable; and I agree that dyes could bleed out into the paint. 

I like your idea of a colored ink underpainting; developing egg tempera first with a layer of ink is an age-old practice.  A shellac-based, “India” ink is most often used because it’s insoluble in water (so initial tempera layers don’t lift the ink), yet doesn’t contain too much shellac (which would cut the absorbency of the gesso, and egg tempera needs absorbency both to manage its water content and adhere well).  Just make sure to apply the​ ink thinnly (if too dense or covering tempera may not behave or adhere); and make sure the ink is actually shellac based (many advertised as traditional “India” inks are really synthetic polymer-based).  Although I haven’t tried them, Sennelier makes a line of shellac-based colored ink. If you try it, let us know how it turns out.  And I’ll let you know if I hear back from the techs at Jacquard.
Koo Schadler​

​I got the following reply from Jacquard technical support.  
The colors are dye-based and the metallics and white are pigment based
What do you want to avoid as far as binders go?  I can’t tell you what it is for proprietary reasons
Waterbased anything doesn’t stick well to pinata, but you could use it over top of tempera with no issue.  The colors are NOT archival