And "-때까지" means "until - happens"

Hope you find this helpful

The most widely known proverb featuring 쥐구멍 would be  "쥐구명에도 볕 들 날 있다".

The Naver dictionary has this about it.

"[속담 (proverb)] 쥐구멍에도 볕 들 날 있다.

몹시 고생을 하는 삶도 좋은 운수가 터질 날이 있다는 말 (Even in a life of severe hardship, there will come a day of good fortune)."

It also has an entry on "쥐구멍을 찾다", which means to look for a rat hole (to hide away from an embarrassing situation).

[관용구(idiomatic expression)] 쥐구멍(을) 찾다.

부끄럽거나 난처하여 어디에라도 숨고 싶어 하다. (Wanting to hide somewhere because of a shame or an awkward situation)

"쥐구멍 볕들때까지" is a variation on the above proverb, like "until we have a good luck (like a rat hole getting the sun)".

볕 is short for 햇볕, or sunshine.  해 means the sun, and 볕 its rays. A similar word 빛 means "light", so both 햇빛 and 햇볕 mean roughly the same thing.

This proverb about changing fortunes seems to have struck a chord with a lot of people in the 1950s and 60s after the Korean War when life was harsh and political turmoil was a constant feature.   So they even made a song out of it, titling it exactly like that, "쥐구멍에도 볕 들 날 있다" (https://www.youtube.com/watch?v=EEHYrBiJnkA).  When your Korean gets good, you can check its wacky old style lyrics for fun :-)