Yes, the blue wire gets pulses from the bike's ignition module so that the pump only pumps when the engine is turning.
The black and green wires are positive and ground, respectively.
The 1986 VT700 has the control relay built into it, which is why it has three wires. The 1983-1985 VT750/VT700s have the relay as a separate module, external to the pump, which is why that pump only has two wires.
You can get a cheap fuel pump at most auto parts stores. But sure it's a low pressure pump, 2-3 PSI. A lot are made for fuel injection systems and run 70 or so PSI. You don't want that!
You can run the pump without that trigger wire, but be warned that if an accident happens, the fuel pump won't stop. It will just keep pumping fuel all over the scene of the crash.
Currently Running Stable:
2010 Honda NT700V
1986 Shadow 700
1986 Honda Trail 110 (Postie Bike)
1987 Honda Rebel 450
1973 Honda Mini Trail 50