How to type the Chinese ellipsis ⋯⋯ using Google Pinyin IME?
I don't use Google pinyin on Linux, but a lot of (simplified) Chinese IME use Shift + 6 to produce ellipsis. I assume the Google pinyin might follow the trend.

And by the way, you can try all the symbol keys on the keyboard with the Chinese IME. They do not always produce the "full-width" version of the symbol on the keyboard. Some Chinese specific punctuations can be inputted in this way.