How is one to understand the wearing of the kippa (skullcap-yarmulke) in light of the following from the Targum [Aramaic translation]? On Judges 5:2 the Targum explains: "The wise men sit in the synagogues...with the head uncovered to teach the people the words of the law", and on Judges 5:9 it reads: "Deborah in prophecy said, I am sent to praise the Scribes of Israel, who when they were in tribulation did not cease from expounding the law; and so it was beautiful for them to sit in the synagogues with the head uncovered and teach the people the words of the law, and bless and thank before the L-rd."
As you note, when the Targum says that Devorah praised the Sages for teaching Torah, it uses the phrase "reish g'lai" "with a revealed head." However, this is only figurative, and not to be taken literally.
First of all, such praise makes no sense. Is there something laudable about teaching Torah while bareheaded? Why would Devorah praise them for that? Second, we find the exact same expression in the Targum regarding a verse in Exodus (14:8): "The Children of Israel went out of Egypt with a high hand." The Targum translates "high hand" as "reish g'lai" "a revealed head." Obviously, this can't be literal. What does a revealed head have to do with a high hand?
One may posit that the Targum intends to explain that when they raised their hands, they knocked off their yarmulkes. However, a more likely explanation is based on idiomatic expression.
The Targum is translating the Hebrew idiom "high hand" into the Aramaic idiom "revealed head." It means, as Rashi comments, a bold, public show of strength. It's like saying, "The Jews left Egypt with their head held high." So too, in the verses you quoted, "reish g'lai" means "a bold, public display of fortitude". Devorah was praising the Sages who,despite their tribulations, taught Torah unabashedly, with their heads held high.
May we also merit to overcome all our obstacles, so that we may learn Torah with an "uncovered head" in the Aramaic idiom that is.