It runs from the PCM, pin 43, gray and lite blue wire. I´ve never traced it, but I imagine there is a connector or two between the PCM and the gauge cluster. It has a common power source and ground with a bunch of other guages. The problem is probably between the PCM and the gauge cluster connector at C-6.
IMO oppinion, a ground through moisture that grounds enough electricity to the tach. to make it malf completely is unlikely, unless there is a little anti freeze or something else present, to help with continuity to ground, shorting the tach signal. Cleaning and drying out the connectors is probably the first step. Possible something else is shorting, another gauge, that is stealing enough juice, off of the common power supply, to affect the tach.
Another posibilty is the ground for the gauge cluster, could be bad and enough juice is backing up, to affect the tach. Though I can´t see how moisture would affect the ground much. My diagram is marked "incomplete" for the instrument cluster ground path, so I can´t help you much there.
My wiring diagram is for a 93, but I beleive it´s close, if not identical, to yours.