tzofeh and tzipui

The Hebrew root צפה has two different meanings.

One means "to look, observe, keep watch, expect", and gives us such words as:

• tzafui צפוי - "foreseen"
• tzofeh צופה - "scout"
• mitzpeh מצפה - "lookout, observatory"

The other meaning of צפה is "to coat, to cover, to overlay." Tzipui ציפוי means "covering, coating, glaze."

Is there any connection between the two meanings?

Klein doesn't indicate any. He provides two distinct etymologies. For the meaning "to look", he writes:

JAram. צְפֵי, אִצְטֽפֵי (= he looked out), Ethiop. tasafawa (= he hoped), New Punic צפא (= seer). cp. also Akka. ṣubbu (= to look at).

And for the meaning "to cover", he simply notes:

JAram. צִפָּא (= laying over, covering).

Not too much to go on there, but certainly no connection is offered. To find some possible theories, we're going to need to go to older dictionaries. Since linguistics was not as developed when they were written, these suggestions are much more speculative. But since there is nothing even in Klein's theory that precludes a connection (like the two roots having clearly distinct origins), it is interesting to read their theories.

Steinberg, in his Milon HaTanach, seems to indicate that the original meaning of the root was "to cover", and the secondary meaning, "to observe", came from the sense "to put one's eye on". If this is the case, perhaps it follows a similar development as the English word "cover", which earlier meant "to put something over something else" and later, in the field of journalism, came to mean "to investigate."

Gesenius says the root means "to shine, to be bright", based on an Arabic cognate. From this, he writes, the meaning "to look out, to view" properly means "to enlighten with the eyes." And he claims that the original meaning of "to cover" was "to overlay with gold or silver", i.e. to make splendid. (Notably, the BDB, which is built on Gesenius, does not mention this theory.)

Jastrow has a similar theory. He also says the original meaning was "to shine." While he doesn't explain the connection between "to shine" and "to look" (I assume it has something to do with light), like Gesenius, he says that "to cover" originally meant "to cover with shining plate."

Finally, Tur Sinai, in a note on Ben Yehuda's entry for the meaning of "to overlay" writes that perhaps this root doesn't mean "to cover" at all, but rather to purify and to improve - "to ennoble" in his words. He then says that this would make the root cognate with an Arabic root צפי meaning "to purify", which is related to another Arabic root צפא, meaning "was pure and clear." If this is the case, Tur Sinai notes, it could be connected to the other Hebrew root, meaning "to see" - which would properly mean "to see clearly." In any case, he summarizes, tzipui in Biblical Hebrew never means to simply cover, but to cover with some better material. 

So did I cover everything?