Conductivity monitoring to detect integrity loss of glass coating of steel
An interesting problem.
I seriously doubt that a continuity test will suffice for your application. 
This would require that you have a large enough fault in the glass surface to actually touch the outer container. I'd imagine that you may have a class of faults that are just cracks or blemishes that could only be detected by a Hi-pot leakage test. 

There are plenty of commercial Hi-pot testers that should meet you need.

If you want to roll your own (inadvisable, though would be fun) then you could use something like a CO2 Laser power supply (20kV) with an optically isolated high side current detector (very high side!!).
The dialectic strength of air is much less than that of glass (though your glass type is not specified). So if you position a high voltage ball probe at 3-4 mm above the glass you should be able to identify high leakage areas as faults.