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As was said by someone above, as thin as possible without "crosstalk" into adjacent wells, and without warping. However, you can think about your design frequency and effective bandwidth (f max and f min) and think about the wavelengths involved. If you have a 1/4" wooden divider, it's going to be high frequency that simply reflects off the face of that. Frequencies within your design bandwidth will still diffuse, but indeed there is a high limit to its effectiveness.
Also interesting to consider that RPG started with aluminum dividers between wells to keep it as thin as possible, but they moved to wood, which while thicker, offered other advantages without adversely affecting the design bandwidth.
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