From my experience with breadboarding of any circuitry, when any uncertainty is involved, one needs to power Off the whole thing, wait a bit for voltage to dissipate, say 10 minutes where a high-voltage coil like that is concerned... then, apply a voltmeter set to Ohms or to Resistance to checking all connections, basically.
Now, clips such as those can often have cold solder joints inside the colored rubber clip cover. Or the solder joint can crack. So I suggest first checking all clips for good conductivity!
And other wires leading to the secondary coil also... check them for good connections.
After that... tell me what the secondary coil is not showing much of... measured how... and I will advise you more specifically.
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