Is there anyway to start/stop a PAL script within another PAL script?

There is not.

Use the Event Scheduler to start the other script at the desired time.

(Unfortunately. That would be really nice to have.)

As discussed many times there is a way to indirectly stop and start a PAL from another PAL by updating a flag in the database and having the affected pal check the existence of this flag status, hence indirectly.

I know that works for stopping, but how would one start a script that way?

The PAL would have to be started manually/automatically to begin with before it can check a toggle to see if the meat of the PAL can run.
There is no penalty for having a looping PAL that checks a toggle to see if it can run.

I'm taking liberties with the word stop, most everyone really means is pause or loop with no action