Older, simpler lights are very simple. Photoflashes, timing lights, and CDI ignitions work the same in some respects.
You have an inverter from12v to high V DC which charges up a fairly large cap. The trigger flashes the strobe, or drives the coil to fire the plug.
The older lights triggers were dead nuts simple. Basically a plug wire which hard wired to no1, ran up into the lamp and connected with a trigger on the strobe itself. This is basically a metal ring clamped around the lamp
What can go wrong. The lamp can fail or break from dropping. The charge cap can deteriorate, although the old Penske's that I have/ had still work / worked (I don't know what I even have, after the house fire).
And the components/ transistors in the inverter can fail. Older ones actually operated via a vibrator instead of transister inverters. The way a vibrator works (used in old tube auto radios) is like a buzzer. A relay with interconnected contacts. it buzzes and vibrates back and forth, and opens and closes SPST contacts (or more) rapidly. This is used to rapidly pulse a transformer to simulate AC. The transformer then jacks up the ac voltage to a high value, where it's rectified and sent to the charge cap, which is connected to the lamp.
LOLOL!!! I went looking for a diagram, and here's AN OLD A BODIES POST!!!
https://www.forabodiesonly.com/mopar/threads/old-school-timing-light.329418/