I don't understand why the 1st order diffracted beam doesn't go to zero when you shut off the drive. My guess is that the standing acoustic wave in the AO crystal needs some time to decay: f = 40 MHz, tau = 1 usec... Q ~ 100. Perhaps, the crystal is damped by the PZT and ther output impedance of the mini-circuits switch is different from the AO driver.

In any case, if you need a faster shut off, or want something that more cleanly goes to zero, there is a large (~1 cm) aperture Pockels cell that Frank Siefert was using for making pulses to damage photo diodes. There is a DEI Pulser unit near the entrance to the QIL in Bridge which can drive it.