From my own experience, both rum and vodka worked equally well. It takes 6 months at room temperature. Of course you can start a new batch every month or two if you use that much vanilla.
I give the whole beans 2 months because the skin of the bean has some essential components of the final extract.
Then I chop the softened beans and put them back into the same liquor to dissolve the resin that surrounds the seeds. This stage takes some regular shaking as well as the 4 months of soaking.
For one batch, I had an extra final step--I added 2 ounces of sugar to a batch with beans extracted with 12 ounces of vodka. The sugar helped to draw the rest of the flavours from the soft skins (they shrivelled up after a month). The entire product was what I would call a "gold standard" for cold extraction--even if there is sugar added.