My Warrior's MX manual has a section on troubleshooting the strobe system and power supply:
https://www.dropbox.com/s/x6lloojwyixstz7/PA-28.Strobe.System.Troubleshooting.pdf?dl=1
That manual makes the same mistake so many others do: checking the voltage at the feed wires, which often have to be pulled out of the supply to do so. You don't get a true reading if they're not connected to that box.
Let's suppose we have a breaker or switch whose old contacts have oxidized (common in old breakers; old switches usually burn). That oxidation is creating a 50-ohm resistance, for instance. The strobe supply needs 2 amps at 12 volts. We can do this two ways: we can divide the voltage by the resistance and see that the breaker willl pass only a quarter of an amp, and the supply won't be happy with that at all, but the meter measuring the voltage needs only a few microamps, or, with my 50-year-old and trusty multimeter, 60 microamps is enough, and it will read pretty good voltage. Or we can divide the voltage by the amps and see that the box has a normal internal resistance of 6 ohms; you can see that adding 50 ohms to it does nothing good for the supply.
Or we can just connect the box and poke a couple of pins through the insulation on the supply wires and turn the system on and measure the actual voltage the box is getting through that bad breaker (or switch). THAT's where the truth is found.
So you leave it turned on and crawl under the panel. This is no fun when you're all stiffened up with arthritis like I am. You clip the black lead of your meter to a good ground. You touch the red one to the bus: 12 volts. OK. Touch it now to the hot breaker terminal and see that it's still good, that the screw is bonded to the bus properly. OK. Still good. You touch the red lead to the breaker output terminal: low voltage means a new breaker is in order. If the voltage is still good you touch it to the switch's input from the breaker, the switch's output terminal, and so on and see if there's a voltage drop there. If so, that switch is shot. No voltage drop?? Go back to the tail and measure the voltage between the pin in the wire that was
negative when you first checked the voltage there, and the airframe, and see if there's voltage of any sort. If so, you have a bad ground. That can be fun, finding that.
I used to teach this stuff to my Aircraft Sytems for Pilots students. I don't know how much of it stuck, but evidence tells me that a lot of mechanics didn't get it or it never sank in. Thye start replacing parts until the problem goes away.