I can only think of three ways to discover which one is intermittently bad. (And I design a LOT of experiments to discover root causes of subtle engineering problems)
1) Wire a sub-fuse to the power wire of each coil, of a value lower than that of the main fuse. That ensures the sub-fuse will blow first. This may not be a good use of your time or materials.
2) Run a
sequential test - putting in one suspect coil at a time. This can take as many as six experiments to find the bad one, and the time each experiment takes can also be variable depending on what your experience was with the time it took to demonstrate the problem.
3) Run a
binary search, which can reduce the number of experiments to two or three, at the cost of more time to change the coils to run the experiment. Try putting in suspect coils A, B, and C. If the problem happens, you know it's one of the three. So take out coil C and see if the problem happens. If it does, then it's A or B, and one last experiment will determine which (3 tries). If it doesn't happen, then the problem coil is C. (2 tries). If the problem doesn't happen with coils A, B, and C, then you know it's D, E, or F, and your second experiment can be on coils D, and E. If it happens, then it's D or E and one more experiment will determine the culprit. (3 tries). If it doesn't happen with D and E, then you know it's F without doing another experiment (2 tries).
Binary searches are particularly useful when troubleshooting or scientific experiments take a long time to run or to set up, or cost a lot in terms of consumables. They are also almost necessary when you have a LOT of variables to consider. I'm in the middle of a problem at work with an opto-electronic system trying to track down about a 1% variation between units that is not calibrating out to a known good standard. I have at least 40 variables, each test can take 8 hours to set up and 4 hours to run, and the customer is screaming at us every day because it's late. Even though the published spec is 3%, they concluded after they bought it that they were wrong and they needed 1% correlation between units. It's a business discussion going on above my pay grade to see how much more they're willing to pay for better units, but it's my job to make sure we can even MAKE better units. Normally I deal with electronic measurements that are 0.05% accurate or so, and the variability of optical systems is pretty frustrating.