Hi,
I agree with the comments about MT1 and the gate. To turn a triac on you apply a drive signal to the gate but it must be relative to the MT1 only. So if you use a battery with a resistor in series, the resistor goes to the gate and the battery other terminal goes to MT1 always. So you apply a signal between the gate and MT1 only.
Now depending on what triac you are using, you may be able to trigger it with either a plus or minus signal. Some triacs only work with certain polarities so you have to check the data sheet.
The polarity of the main power battery however can be plus or minus with respect to the MT1.
So that means you have two polarities (like two batteries) to think about. The polarity of MT1 with the load and main battery and MT2, and the polarity of the gate with respect to MT1 only (the smaller battery).
To test then you should use two batteries. One to drive the load and one to drive the gate (through a resistor). To test the LED with the reverse main battery polarity, simply reverse the battery and reverse the LED, then try using the small battery to drive the gate in both polarities by making the gate positive and then reversing the small battery to make the gate negative.
So that means four tests are required:
1. Main battery forward, LED forward, gate positive
2. Main battery forward, LED forward, gate negative
3. Main battery reverse, LED reverse, gate positive
4. Main battery reverse, LED reverse, gate negative
As Keep mentioned you also have to make sure you use enough gate current but dont overpower the gate either. You also want to look at the hold current (data sheet) because if the LED doesnt draw enough current the triac may turn off when the gate signal is removed (and it should really stay on).