The counter is based on the following trick: whenever rendering is turned on in the PPU, it fetches nametable and BG pattern tiles from dots 0-255 and 320-340 of a scanline and fetches sprite patterns from dots 256-319, even if no sprites are visible. Because of this, if BG uses the left pattern table ($0000), and if sprites always use the right pattern table ($1000), A12 will remain low during all nametable and BG pattern fetches, and high during all sprite pattern fetches, causing it to oscillate exactly one time per scanline and 241 times per frame.