For the most part, if you power up the primary and don't get smoke or a loud grunt sound that means it's not blown up.
Checking each winding for continuity can be done with the low voltage from a multi meter's resistance measurement. Safer than live-voltage tests.
To check the high-voltage winding for leakage to ground, normally you would ground one (usually) red wire only, leaving the other one safely taped on the end. If there's an insulation fault on the high voltage, this tends to expose it. This is pretty much the only other thing that could go wrong besides a dead-shorted winding.
Just one problem. If you don't have a variable-voltage AC supply to turn it up slowly, an incandescent light bulb in series with the primary will limit any potential fault current. The bigger the bulb's watt rating the better. Can't just buy a 200-Watt household bulb any more. I suppose you could put three 60-watters in parallel, maybe?
Once the primary is powered, checking the 12.6-Volt winding for proper output is worth doing. Expect as much as 10 or 15% higher voltage reading when there is no load current. At full load, it will typically drop back down the the specified 12.6.
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