an oudin coil will really be the easiest way. Or any sort of hv supply will work. You can try zapping the anode end with a hene psu if you have one, just don't get too close. Also measure the tube volts before the clicking starts. It should be close to 150vdc when measured between either leg of the cathode and the anode. MAKE SURE to remove the leads before the start pulse, or it will kill your DMM instantly.
Other than that, the fact that it is lasing is a GOOD sign. Just means it is a bit high pressure, which is no big deal once you get it to start. Just make sure to let it run for a while once it gets going.
Honestly, if you plan to keep playing with gas lasers, a BD-10A oudin coil will be one of the best investments you'll make. Even if you don't use it for lasers, it's a pretty cool toy just to have.