The flash is *not* an LED, it's a strobe. It needs to be driven by very high voltage (thousands), which is created by the high voltage driver (that's what makes the faint whine every time the cannon is fired). You can't hook this up to the battery directly. You may also have problems if you try to extend it, as the high voltage can arc between wires or through wimpy insulation at the joint.

The IR & MG LEDs should be easy to extend, as long as you don't mix up the polarity. But, you can't directly connect them to a battery without a current limited resistor inline, 500 ohms should bring it down to a nice safe level (probably dim, but enough for testing). You'd need a digital camera to see the IR LED.
If you have a voltmeter with a diode testing mode, you should be able to test that the LED hasn't blow up or shorted by disconnecting and probing the pins in the connector. You should get a reading of around 0.4-0.7 volts one way.

The recoil unit is probably fed pretty much to full voltage once it's triggered, but my Sherman doesn't have one, so I can't check.

D.