I was unable to rip open the box at the store and examine the wiring.

The clerks were guessing. I gave up.
They're obviously series strung (they're not going to ballast each bulb
individually). How many in a string is a little harder to tell; likely half
are in one direction and the other half anti-parallel. The cheap ones flicker
like hell, so some are likely half-wave (the others may have anti-parallel
LEDs to reduce flicker). Buy a string and dissect it.