Yeah. It originated in the late 1970s when Venables' 'side of the 1980s' was vying for a place in the top flight with Alan Mullery's Brighton side. Both of them made it, but neither stayed there very long. One of my less pleasant memories of the time was visiting the Goldstone Ground to see Brighton outplay us 3-0. Possibly with Peter Ward scoring a hat-trick. But you're right that the extent of the enmity is very odd. I suppose Palace don't have any obviously local rivals in SE London, and they didn't want to stoke up anything with Chelsea or Millwall, so Brighton it was. As for Brighton, I suppose there seemed little point in looking for trouble with Southampton or Portsmouth, who are mutually spoken for.
Talking of which, I came across another odd one when visiting friends in Leicester a few weeks back. Apparently they absolutely detest Notts Forest, which must come as quite a surprise to the latter, who have more obviously local rivals to fall out with. I think the alternative was a rivalry with Kettering, which perhaps would have been embarrassing.
EDIT
Speaking of John Beck, did you see that he's been appointed to a reasonably senior position within the FA? Worrying development, you'd think.