Regarding tsogal, it looks like it should be a participle of a verb tsog, which could mean "to shine" (thus "sunny" is "shining"). To relate this to tsoid, we'd have two suffices, -(o)g and -id, and a base tso, all of unknown meaning. The base tso is certainly unrelated to the genitive preposition.
There is a verb netso 'produce, make' that may contain this same element tso. The difference between this and bahrel 'make' may be that netso involves making similar things over and over. If this is conveyed in part by tso then perhaps this explains the application to types of light, since these are in a sense "propagation" of the same thing continuously.
The idea of "produce" can also be used in English to describe the characteristic result of an action, as in a phrase like mishtahtahv b'netso rebishtah 'construction to produce the tunnel'. If this was a common-place idiom, it may have ultimately worn down to mishtahtahv tso rebishtah 'construction of the tunnel'.