According to the Ford Model A 'Standard Hardware' book there are 2 screws listed for the Ignition (Popout) switch:
Ignition switch to instrument panel screw - No. 6-32 x 9/32" of which there are 3.
Ignition Lock cylinder guide screw - No. 10-32 x 5/15" of which there is 1.
OK. I tried a #6-32 and it would just go about 3/4 of a turn and no more. I tried a #4-40 and that seemed the right thread but wrong diameter. Maybe a #6-40? Mike's sells just the screws so I think that I will call them in the morning. Shipping from GA will be cheaper than to continue a wild goose chase... or is that a Flying Quail chase.