Breakdown, you really can't check. The gate needs 50 mA and that circuit supplies 66. Whoops, maybe not. There is at least one diode drop in there. e.g. (12-0.6)/RThe idea is that the polarity of the supply has to be able to be reversed. You can do that with a DPDT switch AND the gate polarity has to be reversed. One way to do the gate is to use another battery such as a D cell for the gate.
If your below the minimum gate current or minimum load, the TRIAC won't latch. A lot of times there are different specs for each quadrant.
Sensitive gate triacs use a few mA rather than 50. You can think of a triac as back to back SCR's. Back to Back SCR's are actually preferable, but triggering is different.
You cannot detect breakdown without a voltage source high enough. Remember that a lot of tests test for bad things, but not good things. I had a few fuses in my day that passed an ohmmeter test, but flunked a load test. Drove me nuts the first time. The second time I knew better.