George, in the absense of response by Parker experts, I'll attempt to answer.
Original Parker checkered butts are rare. It was an option on D's and above, see the Parker catalogs, but was not a popular option. There are a few are out there, but most checkered butts you see are on replacement stocks for reasons we can only speculate about.
The Parker checkered butts had an unusual pattern as shown below. Most replacement checkered butts were all over checkered. I'm not aware of any determination of percentage, and I doubt it would be possible to determine. My understanding is by the very few I've seen or heard about. The late Rem Parker skeet guns had standard checkered butts, however, there are not very many of those guns.
Here's one I have on a 1911 DHE 20ga, which I understand from others is one of the few known outside of the late skeet guns.
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