you're right there are 24 or 28 threads per inch, which would mean the 28 has the threads tighter together. generally the 24tpi fits one piece crank and 28tpi fits spindles like the redline dimple. my takagi mx one piece cranks take a 24tpi BB, one side has a larger diameter, which would be the lock race for the chainwheel side.
to answer your mongoose question, i'm not 100% sure but they did use a 28tpi BB and yours is probably one of them. they are pretty inexpensive and easy to find, for example i bought a 28tpi for my loose ball redline cranks. it was a Tioga BB-220.