I found a couple quotes from Steve Jobs and Joel Spolsky that I really liked, so I put them in my Gmail signature. I didn't want to forget them as I found other quotes, so I just added them in as well. However, now my signature is longer than the actual emails I was sending, so I, like the question asker, wanted a way to be able to collect my quotes and inject them randomly into my signature.
I couldn't find a working solution, so I held a little mini, solo hackathon in my apartment that started at about 10pm and ended at 3am, once I pushed the code to Github. You can download Random Gmail Quotes from my Github page and install it as an unpacked extension. To replace the quotes I picked, simply edit the quotes.js file -- in your user profile directory -- and replace them with your own. DISCLAIMER: I wrote the extension.
There is another similar Chrome extension on the Chrome Web Store called Random Quotes, but it's two years old and stopped working. However, unlike mine, it has a nice UI where you can paste in your quotes. So, I installed it, figured out what the problem was, fixed it, and submitted a patch to the author's Github account. If you install this one, and you know what you're doing, you can swap out the bsearch.js file with the one I submitted in the issue ticket I created on that author's Github account.
Hope this helps!