Grav pulse comm in hyper
Grav pulse coms do work in hyper, but the range is reduced somewhat. (Note: This is the range within the hyper band in question, not the apparent range in normal-space.)
A pulse is a ripple along the hyper wall, which is the alpha wall for ships in n-space. For ships in hyper, it is the ripple along the next higher wall -- that is, for ships in the alpha bands, it would be the ripple along the beta wall. The various bands of hyper are broad enough that there is more dimensional "separation" between, say, the lowest of the alpha bands and the highest of the beta than there is between a ship in n-space and the alpha wall. This means that the ripple along the alpha wall is effectively stronger for ships in n-space because they are "closer" to it and can "see" it more clearly. A ship in the lower alpha bands might be too widely separate from the beta wall to detect a weaker pulse, and pulse strength falls off with distance traveled, hence the range of FTL coms varies much more widely in hyper than it does in n-space. Moreover, there is more "background noise" in hyper, thanks to the various grav waves cluttering the place up, which also requires greater signal strength. Indeed, a wave is capable of completely blocking a grav pulse if it lies directly between transmitter and receiver.
Grav pulses do not cross the hyper wall in an upward direction. That is, the ripple effect is detectable only from the "down hill" side of the wall. A pulse generated in n-space would be detectable only by another unit in n-space; a pulse generated by a unit in the alpha bands would be detectable only in the alpha bands, etc.