My unflavored 100 mg VG is stored in small glass bottles in the freezer. The nic is very pure, and the VG sets up like rubber cement, but does not freeze solid, and does not expand. After over 18 months, that liquid is as fresh as the day I got it.
That said, my TW unflavored 36 mg PG, which was sitting in the freezer for as long developed a strongish tobacco flavor, probably because the TW nic is not high quality, from China, probably less than perfect extraction and purification, so there were tobacco compounds (actually listed in the ingredients) which will inevitably "bloom" in flavor over time, cold or not, because the PG stays quite liquid in the freezer.
Also from TW, I had some Decadent Vapor 54 mg PG unflavored, also the same time in the freezer. Didn't freeze, of course, since its PG, and also didn't change at all, in color (none) or flavor, since they use pure nic for that.
So I would definitely recommend storing unflavored VG nic liquid, if its high qualtiy nic, in the freezer, in glass. PG, being more mobile, will likely keep longer than at room temp, but depending on the purity of the nic, might turn a bit...probably not enough to reduce the nic significantly though.
60 mL, however, is probably not enough to worry about, other than keeping it in the dark and dry. I generally have a 50 mL amber glass bottle of 100 mg VG I am using for my DIYs, and it can be at room temp for months and be ok.
Plastic for high nic, especially in PG, for long term storage is not a good idea. Depending on the plastic, the PG can leach the plasticizers from it. Glass is best for almost all vaping liquids, for very loing term storage.
Is the freezer overkill? Maybe to an extent, although my obsessive side likes it, and there is something about pulling out another cold bottle for DIY that is very satisfaying because I KNOW it will be as good as when I got it. But much of the reaction with oxygen is from O2 that was already naturally dissolved in the VG or PG using to make the nic liquid, and more is introduced with high stirring when the liquid is mixed. With VG, the freezer sets it up to be so thick that molecules just don't get around much, which greatly slows the kinetics of the inevitable reaction of nic with O2. You can tell this reaction has happened as the liquid will yellow or even brown. No color change at all with my frozen liquid.