Hi John, as a control panel builder in a previous life a "bundle of black wires all black and not numbered" sounds like the stuff of nightmares.
First check along the wires – are they laser marked within their length? Or is that too easy! Some industrial machinery – particularly if it was mass produced – had pre-formed and pre numbered wire looms assembled into it, worth checking carefully that there really isn't some ident system other than the usual coloured ferrules each termination.
Whether there is or no, you are really committed to un-bundling the wires and following individual cores. Messy, time consuming, confusing and difficult to put it all back together neatly. The search and find (battery and bulb) approach will tell you quite a lot, but it can be confusing to differentiate between a cross connection and a "real" connection.
Identifying the power into the circuit and the common return/neutral is a good start, after that think of the control circuit as rungs of a ladder – as they would be drawn in a plc diagram – there can only be a limited number of rungs, and mostly they will be interlocks or contacts in series. Easy to trace if time-consuming. Tag the ones you've sussed with sticky tape and numbers, just as you would expect to see idents if they'd been fitted.
And regular cups of tea. It's going to be a long job! Essentially you are reproducing the manufacturer's cct schematic, so having one of the same machine (even a similar machine) is a good start.
And when you've got all that done, now find the fault. Easier said than done, particularly if the innards of the machine are not familiar! But if it is just a switch that has failed, you can check them off one by one with your faithful battery and bulb, but you are going to have to disconnect the rest of the control circuitry to be absolutely sure exactly what you are testing step by step.
Good luck, Simon
Edited By Simon Williams 3 on 30/03/2016 20:53:27