In Pennsylvania the Fish & Boating rules say it should be an
omnidirectional light.

Not according to the boating manual
There is no requirement listed that the light be omnidirectional. A
reasonable flashlight meets the requirements. That's not to deny that
in some circumstances it might be wise to exceed the minimum requirements.

OK -- change "should be" to "could be" in my statement.

I recall the NJ rules being similar to those of Pennsylvania referenced
above. Do you have any documentation of additional rules for RVR - I
certainly got no complaints when kayaking there after dark.

Only verbal discussions with state personnel stationed there. Also in a
presentation they did a coupla years ago at the Round Valley Roundup. They
did also suggest (see another message in this thread) that sound signalling
devices were also a very good idea because it gets the other boats'
attention and also because it's a wise thing to have on foggy nights.