Sounds like it broke the pin holding the driveshaft to the coupling on the transmission. The reason I can tell is that you say that if you push slightly on the clutch pedal it moves a little bit. When you're applying pressure to the clutch pedal it is pushing the driveshaft back towards that coupling, producing just enough friction to move the tractor. This is a very common problem on both the gear and hydro narrow frames, as well as wide frames and even the Quietlines.
If you are unsure and would like to check and see if this really is the problem, go to the machine, do NOT turn it on, just put it into a gear, and spin the engine over by hand, and watch the rear coupling to see if the shaft is spinning and the coupler isn't. If the pin isn't broken, then it should become hard to turn and if you can turn it at all the tractor will begin to move because it is in gear.
To replace the pin, being a narrow frame machine, you will probably have to remove the rear end from the machine, as well as the driveshaft. I don't recommend you mess with the clutch because it seems like your clutch is perfectly fine. Line up the pieces of the pin, support the coupling where the broken pin is, and use a hammer and punch to drive the pieces out. Then get the replacement and drive it back in, or wait until the machine is back together and drive it in from underneath.

An image of the gear transaxle from an IH cub, the pin is in that little coupler on the input shaft going into the front of the unit
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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)