Coming To Grips With My Grips

I recently acquired a SW 14-3 with wood target grips.  Though I have owned and shot many kinds of firearms over the years this is the first time I have had a revolver with target grips.  The shape with its narrow top and broad bottom feels very different from what I have had before and I have been experimenting with just how to grip it.  At the moment I am only working on single action shooting.

Regardless of the variations I am trying out I have previously shot a handgun best with a tight grip.  I am getting more comfortable with these grips but while reading old threads on this forum I read somewhere that the thumb is not supposed to exert any pressure on the grips.  While I have done that at times with grips that are small for me, it has been while shooting two handed.  It feels pretty strange to leave the thumb unused while shooting with one hand.

Is this relaxed thumb technique a fundamental rule with bullseye shooting so that I should just keep trying it until I get used to it, or should I go with what feels more natural to me; i.e., pressure from the thumb as well as the fingers?

Leave your thumb available to use on the hammer. Timed fire will soon show you that in SA.

Your thumb should be engaged enough to hold the front sight steady in the rear sight notch

I had the same problem you describe.  I bought a set of Nil Grips.  Problem solved.  Those grips are on two of my S&W revolvers, and my Python.  I guess I got used to the "coke bottle shape", sort of, but I predict you will love the Nil Grips as much as I do.

Here are a few:
https://dominionhobby.com/product-category/nill-grips/s-w/k-l-frame/

They are beautiful, comfortable, provide a great grip for your hand, can be customized to match what you want, but unfortunately they are also addictive, and costly.

This is typical of their shape:

Strange as it sounds, the thumb really is just along for the ride. Your two middle fingers provide the front pressure and the heel of your hand the back. Everything else just gets in the way. But whatever you do with the thumb, make sure it is consistent and steady.

My biggest issue when I started shooting revolver for Bullseye was trying to shoot it like my 1911. You need to shoot the gun the way it wants to be shot, with your hand riding high on the grip with the top of the grip nestled in the web of your hand. When I started doing that my timed and rapid fire scores shot up. I have large hands and I find when the trigger breaks, my trigger finger is actually touching my thumb on the other side. It was strange to get used to but practicing that in dry fire took care of that and it became more natural.

Altamont custom builds stocks, and I ordered this pair for my S&W Model 28 Highway Patrolman.

They fit my hand (or vice versa) better than the "Coke Bottle" stock stocks that I removed, and to my eyes, they are stunningly beautiful.  Because they are custom made, the wood grain is used to the best advantage.  The biggest thing, though, is the way they feel in my hand(s).  I better say "hands", as the Model 28 is a very heavy gun, and I don't see myself shooting it with only one.