If it were me I would probably run 4/0 and mount a 100amp double pole breaker to feed it in your main panel. I'd come out of the breaker with #2 copper and then use a barrel connector to transition to the 4/0 aluminum on each hot line.. Then go the 200 ft in a conduit. In theory you don't need it that thick but I bet you would appreciate the less flickery lights when you turn on heavy loads out there.. You could also do direct burial, they make service cable that is approved for burial and you get a higher rating when buried in dirt because it is basically water cooled. 600v insulation, etc. If you make that trade off you may get annoyed every time you kick on a motor on. They make ul approved barrel connectors for the transition from #2 coper to 4/0 and aluminum and Home Depot carries them. The county inspector approved this method for me. I would call your local inspector and ask him. They are often helpful for the Diy folks when not swamped. Try again in early mornings before they are about, and try more than one..
Jeff
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.
Best Answer
Please see my comment on your original question but yes, direct buried cable can be spliced with the correct components. Check with a local electrical supply shop (not a big-box home center) and get their advice on the correct product for your local area and the wire you are splicing. Here is a link to an example of this type of product:
Direct Burial Splice Kit Example