It's a ferro resonant transformer. Behind the steel plate on upper half of the box, there is a large oil filled capacitor. That and the extra winding on the transformer act as a regulating mechanism. (I have the same unit right here)
I'm afraid to give you any instructions because you appear to be not familiar with this type of circuits. There are only few things that can fail. One of the windings can blow or short, capacitor can leak, overheat, or in rare cases, short, or the switch can go. Testing require a live circuit and I definitely won't recommend you'd try it. You said "spark" "smoke", etc. Since I don't see any liquid leaks or burn marks, I'm GUESSING power switch may be the issue. If you have a multi-meter, you can check the switch. Beyond that will be a risk worth not taking.
Are you going to print color or B&W? If B&W, voltage regulation isn't important. Any transformer that is capable of producing the proper voltage and current will do. If you were closer to me (I'm in Central Florida) I'd take you to one of the surplus shops around here and hook you up with a proper switching power supply.
Despite what has been said, most of current Laptop power supply does not use battery as a regulator. If that were the case, you can't operate the laptop without a power supply. (and I can). I also did a load test with what I have. It is certainly regulated. I have a 15 volts 5 amp supply for Toshiba, so I tried it with my Vivitar VI. There WAS a problem. It appears it has some kind of a protection circuit. It won't reliably produce output when lamp was connected. It works if I let it come up to voltage first, then connect. If I keep it connected and power up, it won't. So in enlarger application, it won't work. At least the type I have won't.