聽說兩光=仰光? 有什麼典故?

They are two different things:
¨兩光is pronounced "liong gong" or "liang gong" in Taiwanese.
仰光 is pronounced "giong gong" or "giang gong" in Taiwanese,but many Taiwanese mispronounce 仰 as "yong".
兩光 is an Taiwanese adjetive to describe a lazy bone, a scum in the society, an ridiculous person, a hopless person without doing anything right.
仰光=It was called "Rangoon" before and has been renamed as Yangon which is the capital of Myanmar. Myanmar was called Burma in the past.
兩= two ; 光=empty
The reason why we describe such a scum 兩光 might be because his two pockets are always empty without any penny. (This is only my gussing.)

In English and Chinese Dictionary of the Amoy Dialect pubished in 1883, you can find under Rangoon, it says "liong2-kong1". This shows this particular place name was called so back then around Xiamen. Indeed liong2-kong1 sounds closer to Rangoon than 仰光.

It is likely that people back then thought those from Rangoon behaved in the said manner now we use to describe by using liong2-kong1.

Tim