I see this question: "I am interested in finding out if Parker did make non-auto safeties on these shotguns."
As we see in the patent history, Charles King described in his first hammerless patent how it includes an "automatic" safety.
To reset the safety, there is a rod that is moved by cranking the top lever. That top lever cranking motion uses the rod to push the safety into the "safe" position "automatically".
That rod can be taken out, so now it becomes a "safety" or can be called a "non-automatic" safety.
As I understand the history, there are examples of guns that were ordered without the automatic safety feature. And some are noted as such in the order books.
Who wants it to be "non-automatic"? Commonly, it will be trap and live bird shooters.
If your VHE 20 gauge safety is "non-automatic" then does the configuration of barrel length and chokes suggest it was for trap?
The relevant part is named "safety pin", it is Number 26 here:
Safeties
Hybrid Mode