Should in increase wire size for a well sub-panel?
12/2 may require a 20A breaker

Note ThreePhaseEel's comment, where he notes certain motors require a 25A or 30A breaker (NEC 430.52) yet are permitted to use 12AWG wire (430.22 notably 430.22E), if so, this may have been legal after all.  I would, at least, upgrade to 10AWG until it leaves the house.  I care if it burns down your house. I don't care if it burns down your yard.

If the amp draw is well under 20A, then go ahead and fit a 20A breaker and now you're code legal in any case.  And due to a happy coincidence of the numbers,  your wiring run is almost exactly 1 ohm of resistance.  That means the voltage drop equals the amps.  It's a lot easier to measure voltage drop than amps: measure the voltage at the panel, measure the voltage at the pump, subtract.  The pump must be running while you're measuring. 

Yes, you can run 20A on 12AWG for unlimited length.   Your load might not like the voltage drop, though.  That's why I suspect the actual amperage is well under 20A. 

Don't use a lightbulb for a heater.  Use a heater.

Light bulbs burn out and you won't know when they do. Just go to McMaster-Carr, Grainger, or other industrial supply and buy a heater module. For instance they have a strip heater, 240V, 3 inch wide, 120 watt for $19. Any common strip heater will do fine.  



Or even better, they also sell pipe wrap heating, which you can then wrap with insulation. Could take well under 100W!



There's no way to string 120V out there

The pump has 240V hot-hot-ground 3-wire electrical service out there.  Neutral is not ground so there is no way to obtain a neutral to get 120V service.   No big deal since you can get 240V heaters.   

If you must do this thing with incandescent light bulbs, get 3 bulb bases and wire them in series to 240V.   Then put 3 identical bulbs in there.  Each bulb will see 80 volts (1/3 of 240v).   Since that's 2/3 of its normal voltage, it'll run 4/9 (2/3x2/3) of its normal power.  The bulbs will last a great deal longer, but when one fails, they all go dark.