Yes I think having each string of LEDs "throbbing" as you describe would be what we (my people over here with me) was looking forSo if you had, say, 6 (or 4 or 10) strings of LEDs all "throbbing" independently at, say, 0.5Hz, that would satisfy the effects you need? By throbbing I mean a smooth fade from bright to dim to bright again over the course of a second or two.
I've just woken up and I don't understand what you are proposingThinking outside this thread, have you considered using a remote control device, to have an off-camera technician trigger the electronics on/off, etc... when necessary?
That simplifies the problem from having the prop be practical in terms of controlling the LEDs, to having the effect cued? The practical electronics to drive the LEDs can still be embedded within the sphere, but controlled wirelessly off-camera.