The three pulse bursts are well separated by 0.92msec and the display responds well.
What is the relationship between parameter 500 and the 0.92msec timing?
Why not 500µsec?
Because at 2400 baud ~420us of that 0.92ms is the normal stopbit. Add to that the additional character pacing of 500us.

At 2400 baud you'd also get the same result by specifying two stop-bits.