An important detail is missing. Your spit-saturated paper isn't even remotely similar to solder-mask insulated copper traces.
Take two metal plates and cover each with an insulator (such as a plastic bag, or plastic wrap). Then separate them with 4 layers of writing paper. Measure. Now wet the paper throughly with rain water. (We want to detect rain, correct?) Measure capacitance again.
I hope you'll forgive me for not doing this myself, but rain water isn't readily available here.