My A-series Paragon kiln fires on Low and Medium but not on High.
(The A-series kilns have 4-way rotary switches. You will feel a distinct click between Off, Low, Med, and High.)
Ordinarily, this is due to a dirty Kiln Sitter contact block. This assembly is under the plunger button on the other side of the Kiln Sitter cover plate. If one hot line is not making contact in a dirty Kiln Sitter contact block, the following could happen:
1) On Low, the elements light up.
2) On Medium, every other element lights up.
3) On High, none of the elements light up, because both sides of the Kiln Sitter contact block must carry current for the elements to operate on High.
You can usually solve the problem by cleaning the contacts with a pencil eraser. (Never use emery cloth.) The contact block is not difficult to disassemble if you are careful to catch all the washers and nuts as they fall out of the contact block. A magnetic tool makes disassembly easier.