Hi, and welcome to the forum. I'm not an expert on cameras from the 1950's other than perhaps personal use of a Box Brownie, however a Google search brought up this site that actually covers that serial number pertaining to..., as you believe, an Asahi Pentax S. There's quite a bit of history about them including an estimate of production numbers.
Hope that helps.

Someone on here may be able to help.

Pardon?

I do like it and agree the fence helps with foreground interest. Maybe if the gate was open it would invite you onto the moor?

There's a K-01 for sale on the forum here:
https://www.pentaxuser.com/forum/topic/f-s--pentax-cameras-and-lenses--mz-s--fa-...
That camera is also listed on Ebay at a higher price where it is cunningly disguised as an M42 standard lens. Just goes to show how scarce they are that sellers have to disguise them!

K-01's are scarce because they were only available for around 12 months from Feb 2012 to Feb 2013.
As you are asking about is it any good or popular I'm wondering what you know about it. It isn't a DSLR so those who like a proper viewfinder aren't catered for. Some didn't like the 'brick' design of it and control layout making it uncomfortable to use. But it shares the sensor and general workings of the K-5 so it produces fine images.
It was a controversial camera which some liked and some hated. I guess it didn't sell well, stocks were sold off at half price and then it was discontinued which has made it something of a collector's item.
I'd read some reviews to see if it is a camera you'd love or camera you'd hate. I can't answer that for you!

Take a photograph and look them up when back indoors!. Anyhow, I mentioned a couple of books, albeit long out of print!

Why not just look them up on the web on a site such as https://www.britishbutterflies.co.uk/identification.asp ?

As to books, I've got the Observer's Book of Butterflies, and there's the I-Spy book too.

Is fine tuning an option with non Pentax lenses? I understand that all Sigma lenses are recorded as 'Sigma Lens' so altering it for one lens would affect any other Sigma lenses. The global re-tune would put all the other lenses out.
And yes, it could be a poor copy of the lens so if you like it in principle, but not the results you're seeing, see if you can try another one. I've got a Sigma 24-60 f2.8, an earlier incarnation of that lens and it is really very good but again designed for full frame. It is pretty well inevitable that full frame f2.8 lenses are going to be heavier than similar lenses designed for APS-C wih a more modest aperture. I'm with you that sometimes the lighter combination means you take the camera with you rather than not bother due to its weight, hence I take out an MX-1 or K-S1 with 16-85. It really isn't always worth lugging heavy gear round on a visit to the supermarket!

I paid the intro price on day 1 which was £1599. Present SRS price is £1999 so it has gone up £400. Best ever price was £1499.