Too deep, there are too many unknowns here to give any perfect answer but I will do the best I can under the circumstances to answer your question.
Based on what you say I will assume you have a 12 volt tractor that uses a 6 volt coil with an external ballast resistance (or wire or thermistor) plus a start by pass system that applies unballasted battery voltage to the coil ONLY when cranking THATS HOW I WILL PROCEED IF THATS NOT WHAT YOU HAVE THIS IS DIFFERENT.
YOU STATE:
Battery voltage 12.34v
Battery voltage with ignition on 12.05v
RESPONSE
Since the ignition system ONLY draws around 4 amps with points closed (as normally are) that doesn't sound like any real good strong battery HAVE IT LOAD TESTED AND INSURE ITS WELL CHARGED
YOU STATE
Battery voltage when CRANKING 10.15v
RESPONSE
Unless the starter is bad drawing excess current, again that don't sound like any real good strong or adequate CCA battery
YOU STATE
Voltage at coil with key on 3.9v Really scratching my head there. Why only 3.9? Don't I want all 12 or at least 10.15 at the coil?
RESPONSE
With key on and points closed (as they are normally when engines not running) IFFFFFFFF its a 12 volt tractor with a 6 volt coil and series ballast resistance (or wire or thermistor) ID EXPECT MORE LIKE 5 TO 7 VOLTS so that 3.9 sounds like the ballast resistance is too high or the resistor or thermistor or resistive wire is bad or one of the connections is bad and/or resistive dropping voltage. THERE MAY BE A BAD OR LOOSE OR RESISTIVE CONNECTION IN THE IGNITION AND BALLAST CIRCUIT THATS DROPPING VOLTAGE!!!!!!!!!
ALSO a bad resistive ignition switch can be dropping voltage with ign on and points closed, hot wire the switch to by pass any resistive contacts and see what happens
NOTE to test the ballast by pass system (If it has one) see what the coils input voltage is WHEN CRANKING !!! When cranking it should rise way above that 3.9 volts you measure when its just setting there with ignition on. Again it may be a bad resistive ignition switch.
NOTE I cant say from here if you have a ballast or 6 volt coil orrrrrrrr some have a thermistor resistive ballast versus a regular discrete ballast and some have a resistive wire that's temperature compensated that starts out at low but then higher resistance once warmed up.
HOWEVER 3.9 volts on the coils input with points closed and ignition ON SOUNDS TOO LOW FOR A 6 VOLT COIL (if that's what you have??) and I suspect a bad ballast or bad thermistor or resistor wire or a bad connection or bad ignition switch causing that such low 3.9 volts.
Try to hot wire voltage to the coils input to eliminate any bad switch or bad connection or bad ballast problem to get coil voltage up and see how she starts????????????????????? Don't let it run too long if its a 6 volt coil !!!!!!!!
HAVE BATTERY LOAD TESTED,,,,,,,,,,CHECK ALL CONNECTIONS,,,,,,,,,,MEASURE COIL VOLTAGE INPUT WHILE CRANKING,,,,,,,,,,,,,,TRY TO HOT WIRE COIL DIRECT TO ELIMINATE ANY SWITCH OR BALLAST PROBLEMS
YOU STATE:
Why only 3.9v at coil though?
RESPONSE
Bad ballast or bad thermistor or resistor wire or bad resistive ignition switch (try hot wire)
John T Long retired Electrical Engineer and rusty so no warranty