I am not sure, what you mean by "... start and stop the BSP clock". Do you mean, that you BSP should be set to "internal clock", but you want to play/stop it through an external analog signal?
I think you can do something like that if BSP is a slave, as described in the manual:
If Sync is set to an external source and a TRS connector is used, BeatStep Pro
will follow the master and will:
◦ play when it receives a high state signal and clock,
◦ pause with a high state signal and no clock, and
◦ stop on a low state signal, with or without clock.
So use a 1/8’’ stereo (TRS) cable, send the clock on left channel, the pulse signal to start (high state) and stop (low state) on the other. But it won't start the BSPs internal clock independently...