Hey there! I too am starting my first batch of pineapple vinegar after a lot of research at the library and on the internet. As expected, there is no standard answer to your question -- and I am in no way an expert as this is my first time -- but what I've read is...
There are some batches of pineapple vinegar that have been cultivating for years. You can continue to cultivate by adding more food source for the mother, as you go along.
I sought out organic pineapples to start, as I had read that commercially produced pineapples contain formaldehydes that make the commercial pineapples that are sold, "pretty".
I used a clear, large, sterilized glass jar with a glass lid, but actually wrapped the top with 3 layers of cheese cloth instead of using the lid. I wrapped a dark towel around the outside of the jar and just have it sitting in a corner, away from everything.
I started my batch on July 20th and have noticed I have bacteria on the surface of the water even though the pineapple is submerged and weighted down. I'm crossing my fingers that all is well and that nothing in there is harmful.
I've read that when you see a separation line (vinegar on the bottom and the rest is up top still "working" you can begin to use the pineapple vinegar from the bottom. The trick is getting it out without disturbing the mother that is growing on top!
Beyond all of this, I've read that you are just supposed to taste from time to time to see how you like it. You must continue to "feed" the culture by inserting a new source of sugar so that the bacteria can thrive. I assume that means more pineapple or more sugar and only after a few months at a time, I think.
Glad to see a recent post on this subject and to have someone who is also a newbie! Please post your results as you go along and I will do the same.