The center distances would most commonly be left accurately at the calculated seperation distance. Backlash is created by a slight overcut of the gear tooth's whole depth.
Commonly, one will use a gear tooth vernier caliper to measure the chordal thickness of the tooth right on the machine. However, these measuring tools do have limits on how small of a tooth they will measure. If you cannot get a caliper in to the pitch circle depth (the addendum deep), then you'd probably need to spring for a 3 wire measurement across the gear. There are tables or formulas in Machinery's Handbook to help you figure the pin diameter and the chordal measurement, so that you can infer the pitch thickness of the gear tooth based on how far a wire of a particular diameter fits down into the gear tooth space. The ideal wire is calculated to make contact near the addendum depth, which is where the pitch circle is located.
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