An enclosure is a very different thing to a solid piece of material which is optimised for the particular function.
IMHO,the permittivity of the volume of air inside the enclosure would be dominant,with the very small volume of plastic in the enclosure walls having a minimal effect
There would almost certainly be no conventional resonant cavity effect,as the plastic,even if it ceases to look like a good insulator at high enough frequencies,will look like a very lossy conductor.
Dielectrics can be just as reflective, in fact moreso*, than conductors! My "hall of windows" example is relevant, indeed exact -- considering light is EM, just not coherently resonating, as we are looking for at RF.
*Check out "supermirrors".
A typical example might be ABS, having a wall thickness of 3 mm, dielectric constant of 2-3.5, loss tangent 0.5-1.9% (unstated frequency), in a 12 cm box.
The wall thickness is effectively sqrt(2) to sqrt(3.5) times thicker due to refraction, or 4.24 to 5.6 mm, which has a 1/4 wave reflection at 17 to 22.4 mm wavelength, or 13.4 to 17.6 GHz. This would be about 75% reflective. At double this frequency (i.e., half wave), it would likewise be extra transparent. At inbetween frequencies, it will be a little over half transparent, and at very low frequencies (< 2 GHz or so), very transparent.
The box being about 12 cm across, suggests 5-7 wavelengths could be contained within, for resonant modes along that axis. There will probably be one or two peaks and/or valleys where the wall reflection and cavity resonances coincide, and the energy inside the box will be several times greater (like I said, probably about 10dB, or less), assuming some means to couple energy into the box of course.
Regarding loss tangent: since it's not mentioned what frequency it was measured at, it's impossible to tell what might happen. There may be molecular relaxation frequencies near the 10s GHz range, which would not only kick out lots of losses, but change the phase shift and dispersion along the way. The reflectivity is unlikely to be any higher, so that the cavity mode peak might be only 3dB instead of 6 or 10dB, for lossy materials. Take the lossless estimate as a ceiling figure, I'd say.
So -- if you're talking about more modest frequency ranges, you're absolutely right, it's simply not big enough or thick enough to contain resonances in the < GHz range -- but taking the EM spectrum as a whole (at least up to THz), some at least mildly interesting behavior will definitely be present. Whether the OP was interested in the complete account, or just a more practical range**, I don't know...
**Amateurs I don't think are playing much in the 10s of GHz... but with bandwidth ever on the rise, it's getting more and more practical to consider these sorts of frequencies. Not to mention already old standards like sat comms that operate in those ranges.
Tim