You're heading in the right direction. Especially, with a 10 year old heater that's never been cleaned.
Using a vacuum (a shop vac is great for this) that has a hose and brush attachment will do the job. Also, canned compressed air with a straw nozzle (like you clean your computer with) can be used to blow out the pilot tip and reach areas the vacuum can't.
After you've cleaned the heater, check for wear and damage to any of the internal parts. Especially, any wiring that may look burned or frayed. Also, be sure that the exhaust vent damper is working properly and the exhaust vent piping is free from obstructions. The clicking you heard may have been from the automatic safety damper switch.
If after 10 years you can't find your Owners Manual, here's a link to it. It will assist you any cleaning the unit and spot any problems.
http://www.empirecomfort.com/EMPIRECOMFORT/pdf2009/manuals/12425-1008GWT.pdfGood luck and remember to clean the wall heater annually.
Rich