The plastic handbrake grips do split as they age. The leather ones don't seem to.
@A2Steve,
@Clackers do either of you have one available?
At some point in the production run there was a change to the way the grip attaches to the plastic cover of the handbrake lever. Earlier ones have two small holes on the underside of the plastic cover, which you poke pins or wires through to detach two barbed plastic tangs inside which are on the end of the grip. Later ones have one larger, more oblong hole which will take a small screwdriver, the grips for these have a metal clip inside. Once the grip is off, the plastic cover just pulls off too so you can always replace both to get the correct fitment.