I am going to watch this thread as i am in a similar situation.
I found another thread in this forum about making lock tumblers accepting different keys. So they must come out of the lock somehow.
Have you tried flushing out your lock with WD 40 and brake cleaner? Sometimes a lot of gunk can form in the lock tumbler. How does your key look? Maybe it needs replacing?
The things that make your switch click is most likely a tiny springloaded ball, moving from indent to indent as you turn the key. If the ball and spring got jammed up in their barrel you cant feel the indents, also, if the indents are packed with dirt you wont feel them either.
As with all switches: watch out for the tiny coil springs, once they pop out of position, they are gone forever.
If you peel back the rubber cover, you should be able to see the cables being held/clamoed with a metal brace, riveted to the plastic body. Gently pry it open to release the cables. The you have to fiddle with the two tabs holding down the plate with the soldered copper contacts. Unhook them to get the plate out (watch out, springs on the other side, and very delicate copper contacts!). Once the plate is out you'll see the disc which is rotated by the lock tumbler. In it must be the ball & spring for the click mechanism.
At least if my memory serves right... i did this on an old SL 125 with wonky contacts.
Clean everything, grease very lightly, and reassemble.
Do you have pictures of your lock and key?