Additional information: There are three wires from the ignitor switches to the spark module: Yellow (common), Red (oven switch), Blue (stovetop switches). When I disconnect the Yellow/common wire from the spark module, and reconnect the power there is no clicking. If I disconnect just the Red/oven wire, there is still clicking. If I disconnect just the Blue/stovetop wire, there is no clicking.

Am I right in concluding that one of the stovetop ignitor switches is bad, or could this still be a spark module problem? If it is one of the switches, I assume I have to swap in a new switch for each of the four burner controls one by one to isolate it. Are the wires on this model soldered on or do they use blade connectors, in which case I can just pull them off and test the switches in place? Since it isn't a simple matter of just looking (I'll have to disassemble the front panel), I'm hoping someone might be able to answer before I start taking things apart.

I'm answering my own question, just so that anyone else with this problem will known what's up.

I found another suggestion on the web that it might still be moisture, and to try a hairdryer. I ran a hairdryer on one of the switches for a minute, and the resistance jumped from 600kohm to 1.9Mohm, suggesting that it really was moisture. I ran the hairdryer for 2 or 3 minutes on all of the switches, and there was no longer a measurable connection when the switches were open!

I then reinstalled the switches, reassembled my stovetop, and everything worked great.

So, if your burners keep clicking on your stovetop, I highly recommend using a hair dryer to dry the ignitors and the switches before taking anything apart or panicking or buying new parts. It can't hurt, and it just might solve your problem!

I have a thermadore with igniters, I thought the igniter went out.
After my experience I am now convinced it was just the insulation on the wires that went bad. Here is how it happened:
First I had one burner that would not ignite, so I ordered the parts and put the new igniter in.
I tested the old one by moving the wires around, Having taken a digital picture first so I could get back to my starting place.
Everthing worked fine.
I closed up the stovetop cabinet and they all worked for about a week, then I got some clicking, then a burner igniter stopped working altogether.
I opened up the stovetop and put coiled insulation around the wires and all worked again. Then first one then three of the igniters stopped working and the one that did work started clicking.
It is a pain to get to the wires, I have to pull the asperators out to get the case open
So it seems te real problem is bad insulation around the wires. The igniter must work only when it sees an open circuit and when the burner lights the ionized gas looks like a low resistance. When the insulation goes bad, the igniter see a low resistance, and they don't work.
That is my current experience: replace the wires first, then the igniter if needed, test things by moving the wires from one igniter to another to see if a the circuits work, or the igniter module works. Mine has four igniter coils in one molded case, and each igniter coil looks at a different burner
I bought the new igniter, tested the switches on the knobs by moving the wires over to another switch
I put the whole thing back in and it worked for a while, then one after the other started clicking, some didn't light, one clicked inside the burner chamber, not at the spark ignition area.
.so I put curly wire separator binder around the ignition wires, it worked for a couple of weeks, then threke of them quit again.
I bought new wire from McMaster.com a great mail order commercial parts place: Wire 8296K16, 30,000 volt 302 F degree high temp wire. about $ 2.50 per foot. and a pck of crimp connectors: 69525K11, .110 "w by .02 thick tab, pack of 100...about 10$. They are all working now.