Fred Y

Hi again Neil, Mark, Bill,
Thank you all for your advise with my Duncan Kiln situation.  We have discovered that the LT 3K Dawson Control Panel/sitter is not old, and need replacing.  I have a new thought... the actual Kiln body is in great shape [bricks, coils, top, etc.].  I have contacted Skutt Corp. Technical Dept. about the possibility of replacing the entire control unit with their new, Skutt Kilnmaster Touch Screen controller.  They have videos on their website explaining retrofitting that unit to non Skutt Kilns.  IF that were possible [I havent heard from them yet] it would be a very cost-effective way to have a virtually new and safe kiln. I paid $400.00 for the Duncan Kiln with the Dawson Controller. The Skutt Touch Screen unit is about $600.00.
We have a friend with that Skutt Touchscreen and [attached to a new Skutt Kiln] she raves about it.  Any thoughts still appreciated!
Fred
ps:  I've attached 2 photos of the insides of the kiln...

It's not just a knob. It's specific to the Sitter, as it has a piece on it that triggers the shutoff. Google 'kiln sitter timer knob' for sources.

Thanks! Your maintenance manual here https://aakilns.com.au/pdf/Duncan_Kiln_Service_Manual.pdf but if you have never fired a manual kiln, there are some steps to learn and detailed in the operating manual below.
This is a 24 amp kiln and the manufacture specifies 30 amp breaker, 40 amps is too large per the manufacture and North American Code.so this should really be protected with a 30 amp breaker Page 58 of 75 in the maintenance manual, bottom right corner of the electrical drawing show amperage, wire size and breaker 
This is a manual kiln that requires the safety countdown timer be set for some period greater than the time it will take to fire. So if the firing is expected to take 8 hours, the timer must be set to something greater such as 9 hours. It is for safety and if it is on or reaches zero your kiln will shut off. Did you set the timer for something greater than zero when you tested? The kiln sitter to be activated  using an appropriate cone and then arming it by depressing the plunger  Page 7 and Page 28 -33 Did you place a cone in the sittter and depress the plunger? Finally the two knobs are turned up gradually throughout the firing (they are know as infinite switches )such as two hours on low, two hours on medium and finally to high until the kiln sitter shuts off the kiln. Page 21 - 24 The manual above provides maintenance for all the components, operating this kiln is better described here https://eadn-wc04-7751283.nxedge.io/wp-content/uploads/LX851_Duncan_Energy_Saver_Owner_Manual.pdf
Last note, this kiln is rated to cone 8 if firing to cone 6 routinely you will get a moderate number of cone 6 firings before the elements will need replacement. Cone 10 rated kilns provide considerably more firings before element replacement when routinely fired to cone 6. The maintenance manual has element resistance measurements listed. If the elements have risen by 10% in resistance, it’s time for replacement to make cone 6 temperatures.