My students apparently use the power supplies on all our scoring machines as yo-yos, and predictably, we get problems.
The question: if we are splicing a new plug/socket onto the transformer, how do we tell we are connecting the right wires?
If you still have any intact power supplies then you can always use one of them to determine the correct polarity. Or if you have any plugs with some of the wire still attached you may be able to sort them out by examining the wires - manufacturers will often mark one side of a two conductor cable with a thin white stripe in order to make it easier to keep track of which side is which.
If none of that works, the FA-07 user's manual has a diagram showing all the connections on the back of the machine (I'll try to attach a copy). The power socket is shown in the lower, left-hand corner and if you zoom in you can probably see the polarity for each pin (when facing the socket with middle hole (#3) to the left, in the 9-o'clock position, the lower hole (#2 - in the 6-o'clock position) looks to be positive and the upper hole (#1 - in the 12-o'clock position) looks to be negative). The is probably standard for all Favero machines.
The good news is that most machines these days are pretty well protected against reverse polarity so while the machine may not work if you get the poles reversed you aren't likely to actually damage anything. And Faveros are probably among the most robust in this regard (the FA-01 and FA-05 can even run on 12 V-AC).
edit: What I can't understand is why Favero uses a 3-pin XLR connector to begin with when a coaxial power connector would be smaller, lighter and probably have less potential for shorting the pins together.
DIN connectors can be had with locking rings. They would be more appropriate as power connectors than XLRs. XLRs however are more rugged than nearly anything else.
We have five of the Favero boxes and all five of the power supplies have gone the same way. Trouble is, the problem tends to be right where the cable enters the block. I've had limited success taking a hacksaw to the plastic block and cutting it open along the seams, then splicing in a piece of slightly heavier cable - same stuff as I'd use for repairing body cords.
Success was, as I said, limited. This was in large part because there are two very fine connections to the cable from the out side of the transformer - they seem to be very soft and easily broken, I assume intentionally so, acting as a fuse.
To replace the ones I destroyed, we went around the local thrift stores looking for orphaned power supplies of a suitable voltage, and married these up with some cheap XLR (microphone?) connectors off eBay. I'm not sure whether we had problems with polarity or not, but I know I did test to match with a working power supply by plugging them in, hooking my multimeter up to two jewellers' screwdrivers and inserting them into the XLR connector.
As a prophylactic measure, given that breaks further down the wire are so much easier to deal with, I folded the first few inches of cable against the body of the power supply and taped it down, so that now the stress point is well away from the entry to the casing. Now, if there's a break, it's a simple cut and splice rather than open heart surgery.