That sounds like a bad switch to me, unless the wire from it to the coil is bad somewhere. It could be, but assuming the wiring is good like you say it is, don't think there's anything else that can cause that thing to happen.
I say, replace the switch, if it isn't the issue, well, at least you've saved yourself from having to replace it later
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'70 107 with k301 engine swap
'71 106 with 38" deck
'70 147
R with factory replacement k321, 42" deck
'61 Original with 38" timed deck
'63 70 "pinkie"
1863 with 54" deck
'46 Farmall H, '50 Farmall Cub
105 x2 (parts)