Gas cooktops that click without lighting, induction zones that cut out, and radiant elements that only work on high. Three different faults with three different fixes.
Almost always a wet or dirty spark electrode, or a burner cap sitting slightly out of position. Dry everything thoroughly, clear the ports with a pin rather than a toothpick, and seat the cap properly. That is free and it works often enough to be worth trying before anyone comes out. If it still clicks, the ignition module or the switch is next, and that is a technician job.
A radiant element that only responds on the highest setting has usually lost its infinite switch, not its element. An induction zone that starts and then cuts out after a minute is normally an overheating fault, either a blocked cooling fan underneath or a failing power board. Induction repairs are worth diagnosing carefully because the boards are expensive and often blamed unfairly.

Dry the burner cap and electrode completely and clear the ports. If it still clicks after that, the module or the switch has failed.
The glass itself is replaced rather than repaired, and on some models the part costs more than the appliance is worth. We will tell you which case you are in before you commit.