If you use a T-handle tap wrench in a lathe, mill, or drill press, it really should be fitted with a guide pin to keep it from stressing the tap laterally since that is a major cause of tap breakage. You can buy guided tap wrenches commercially but it's a simple job to make your own.
Drive the handle out of the wrench and bore a bit of metal (I used brass) to fit over the head of the wrench. In the end of this chunk drill a hole to be a nice sliding fit on a short rod (I used 1/4" drill rod). Crossdrill the brass to accept the handle. Assemble and drive the handle back through to lock the brass onto the wrench. I leave the guide rod unrestrained but you can add various devices to restrain it if you wish; I don't find it necessary.
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