How to measure magnetic choke type ballast to veryifyi that the coil is not shorted out without trying it out with lamp? Regular ohm meter will do for finding out if it's live to earth fault or if the coil has break.

Quite nice method is a resonance ringing tester: You create a fast pulse into a coil under test (e.g. a mosfet switching the coil to a DC supply for few us) and then count how many times the resulting ringing crosses zero. Danyk (danyk.cz) aka DiodeGoneWild designed such ringing coil tester and I guess it will be also published. He made it using some microcontroller, it could be done using common counter IC's (up to 100 is enough).

The idea behind is, whatever the inductance or coil design is, if it is good, the L, parasitic C and losses would form high enough quality factor to register a significant number of ringing pulses. But if there is some internal short, the resulting partial short circuit effectively increases the losses so much the Q falls down and the number of ringing pulses gets significantly reduced. The various coil parameters (if it is in H or uH) changes the frequency, but usually the Q factor, so number of pulses on a good coil uses to be very similar (few 10's) across most practical inductors.

You may do the same manually using an oscilloscope, small cell battery and a contact: Momentarily connect the coil under test to a 1.5V AA cell and observe by the oscilloscope how many ringing pulses you see.

There is no direct number to determine good vs bad, but the method is very sensitive to compare good reference coil vs a questionable one.

https://www.youtube.com/watch?v=E1dopmxph2A
https://danyk.cz/avr_ring2_en.html

Well, from the practical point, the easiest way to test choke type ballast is just to hook the choke across full line voltage and measure the current. It is OK, because most lamp circuits start at practically short circuit across the lamp (starter closed with preheat fluorescents, cold HID burners with low voltage). Generally, you should expect about 1.5-2X nominal lamp current.

If the ballast is in bad shape and you have the reason to think the winding may be burnt/shorted, you shall use some current-limiting device in series. A sensitive fuse or circuit breaker (~6A) or high-power incandescent lamp is a good idea, to avoid fireworks

Running the choke for about a couple of minutes shall not cause serious heating or smoke if everything is OK.

Next step is to hook up some junk lamp, let it run up and check if the circuit current equals design one for that type of lamps.

Measuring coil inductance with a proper, but low power LCR meter usually gives some idea about the inductance/resistance/Q factor,too, but for iron-cored coils the results may be somewhat off because of the core non-linear behavior at small signal.

The thing is, if there just few turns internally shorted, you won't see it directly on the current. The only thing that may be somewhat observable are the losses. So if you have some real power meter and a known good choke of the same type, after checking the direct connection to mains (there should be about 1.5x the nominal current), you may check the current (to check the ballasts are indeed the same type) and mainly the real power with some lamp. If the current is similar but one consumes way higher real power than the other, chances are there is an internal short circuit so it is bad.

Other option is to connect a known good ballast in series with the questionable one and the whole thing to mains. If both are good, the arithmetic sum of voltages across each ballast would equal the mains (because both ballasts would have very similar phase shift - both are slightly lossy inductors). But if the sum is greater than the mains, it means there is a phase shift between them, so most likely one of them has an internal short between turns. This works alsowhen both ballasts are not exactly the same, nominal currents should just not be more than about 30% difference, so you won't drive either of them into saturation (where mainly the harmonics may create extra rms voltage across each of them that won't sum up correctly so you get false fault result).

Other option is to connect it in series with a known resistance (e.g. an incandescent lamp, where you may directly measure its V and A; this incandescent is there to have something to prevent going to core saturation while still be able to extract its exact parameters from easy to measure values), then measure the real power this whole contraption consumes. Because this power must be P=I^2*(Rlamp+Rloss), you may calculate the corresponding Rloss of the ballast. And because normally the vast majority of the ballast losses are the ballast winding resistance, you may compare that with the real winding resistance measured by an ohm-meter. If the calculated Rloss (from the test circuit) is comparable to the winding resistance or mainly higher, you have very likely a bad ballast. This method is useful if you do not have a good reference ballast for the compare.

It is impossible to have a single or small group of turns shorted in a ballast choke for any significant time. Insulation on the adjanced turns will quickly burn off too, and the problem will escalate to a full short because of significant local dissipated power. The choke either works, or is burnt. Even if for some reason the ballast demise is delayed, lamp current will be certainly abnormal. Absolutely no way to have short turns in the coil while the lamp current is still within design limits.

May be somewhat possible in neon transformer secondaries, when very thin wire is in use. I believe I have seen this once.