There are several ways to work with the glazing idea.  Here are a few random thoughts....
1) It is common to do the underpainting with either Biobased Artist Thinner or Oil of Spike Lavender.  These thinners will evaporate fairly quickly and get out of the way, without leaving an overly thick oil or resin layer.  For the glaze part of your work, however, Oil of Spike Lavender is preferred over Biobased thinner.
2) When using any form of damar or copal you are working with a resin.  Canada Balsam serves the same general purpose, but it is in sap form so there are no resin crystals.  Resins and Balsams dry fairly fast, and are relatively transparent.  That's why they are popular for glazing. Canada Balsam dries so clear it was used historically to glue microscope slides together.
3) Some pigments are more transparent than others.  Titanium White is extremely opaque.  However, most pigments can be used for glazing if thinned adequately.  Keep in mind that the amount of pigment will vary greatly: phthalo green and red 254 will do it with the smallest amount.  Iron oxides will sometimes require a tad more.  Experiment.
4) A water-washed oil is thicker and dries faster than regular oil.  Walnut oil is clearer than linseed.  When glazing, it is good to always have enough oil as a binder.  Too much resin can result in cracking.  Resin doesn't count as a fat in the "fat over lean" equation because it is not as flexible as oil.
5) Turpentine, as sold on the market today, is often a petroleum mix - petroleum is used in the distillation process - and turpentine is regulated by OSHA.   Turpentine, according to the Toxicology Data Network: "If inhaled, will cause nausea, vomiting, headache, difficult breathing, or loss of consciousness."[email protected]+204
Oil of Spike Lavender is a direct replacement.
For glazing, you might want to consider a mix of spike/balsam/water-washed walnut oil.  But there are 100s of other ways to do it.  Much of the creative fun comes from individual experimentation.  Just be sure to use enough oil so that you have a solid binder.