What's a good resource for basic pulse transformer design. What does the pulse number (12, 18, 24, etc) mean? Is it just the number of pulses delivered to the xfmr primary each period?
You mix up two different things, just because both contain the word pulse.
Pulse transformer: small signal transformer (but with high isolation capability) to transmit a trigger signal to a thyristor.
Rectifier circuits designed with different pulse numbers:
The number refers to the number of peaks in output voltage you get for one full periode of the line frequency.
From a three-pahse line you can get 6-pulse rectification without a transformer. For the higher pulse numbers you need special (power) transformers, called rectifier transformers or converter transformers.
The only connection between both things is that your BOM for such a rectfier will usually contain the number of pulse-transformers as provided in the name of the rectifier circuit.