On Tue, 10 Dec 2013 23:05:40 -0500, Rick wrote:

I did hear some snapping at one point, but then it went away.
It was like a sharp click click click...

That's the igniter...

Ah. That must be this thing:
http://farm6.staticflickr.com/5493/1...04b85a9f_o.gif

The funny thing is that the PDF didn't say what caused the igniter to
start snapping. I guess I'll read the PDF again ...

Ah ... found it... It must be the thing called the "pilot igniter".

Here's what the PDF says about it:
"When the thermostat calls for heat, the control circuit is closed
between the terminals R and W. Power from transformer TRAN through
fusible link FL, limit switch LS, and vent safety shut-off switch
VSSS, energizes the pilot valve part of automatic gas valve GV and
*pilot igniter PI*. The pilot valve opens, permitting gas flow to the
pilot burner where it is ignited.

So, I guess that snapping was from the "pilot igniter".