Here's the vibrato arm installed in the freshly threaded hole.  I found that a nut backing a washer and strong rubber washer could be set to clamp down when the arm was swung into playing position, yet could be swung counter-clockwise out of the way which would back the threads out and thus release the rubber washer's mild clamping pressure.  See the vibrato installed on the guitar HERE.
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Kay Silvertone 1417
c.e. 1964

Cleaning up the vibrato roller's arm-socket threads:

UNDER CONSTRUCTION
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This page's text is temporarily brief.  I will expound with more as this guitar cleaning up process proceeds.
Feel very carefully with the 10-32 tap to find and ensure it's alignment with the old threads.  The tap is tapered on it's business-end for several turns and will most often align the tap with the old threads.  Often we can get the tap started with our fingers;  Otherwise the tap will have to be started with the tap-handle being used.
On some jobs I'd rather use hand-palm size vice grips as a tap handle.  Clamped loosely the vice grips will articulate to hand positions and also give an alignment and cutting feel feedback.  When we start cutting we go slow and careful and feel the alignment and cutting feedback from the tap.
Turn the tap only 1/16 of a turn in then out a couple of times to set and clean the threads before cutting another 1/16th turn.  When the tap's taper is all the way in the hole and the full width having cut about 2 full turns and the progress feeling OK, then we can increase the turn to 1/4 turn in and out for each cut until the taper fully exits the other side end of the hole.  Any time the cutting doesn't feel nice, easy and smooth, ....then stop and make sure such resistance is normal for the old threads conditions.
Continue to cut until the tap reaches about 5 thread teeth from the end of the thread teeth.  These additional turns help reform the threads well and clean them out.  Then turn the tap in and out 2 full turns several times, and remove the vice grips for the next step.
Use fingers to turn the tap in and out a few complete turns to finish cleaning out the threads.  If the tap feels "snaggy", then simply wiggle the tap slightly in the hole while turning it with fingers.
I put a machine screw into the hole to hold parts I will use for putting locking stop-nuts on the vibrato arm so that it can hang downward loosely when desired and swung into a preset position when desired.  Having a machine screw in the hole will protect the threads from other tools still to be used to clean up this roller bar.
Here's the vibrato arm installed in the freshly threaded hole.  I found that a nut backing a washer and strong rubber washer could be set to clamp down when the arm was swung into playing position, yet could be swung counter-clockwise out of the way which would back the threads out and thus release the rubber washer's mild clamping pressure.  See the vibrato installed on the guitar HERE.