Nope. Soldering isn't an option. The brass colored original pivot is actually a plated steel (cad or chromate), and the casting is either aluminum or zinc.

Out of curiosity... Why? Is yours loose too?

It is mushier than I would like. I don't have the machining skills to make the replacement part so I was trying to see if there was another way to tighten up the existing brass part.

Mine was mushy and actually smoked when on for extended periods. I went through it twice. I then bought one from Dave Irwin (traded mine in). It's been great since.

I just had Dave Irwin rebuilt mine. Better than new.

In my search for wiper wiring continuity I rememebered this thread, I had to take my steering wheel off anyway because it was in the wrong place slightly. I found that even after cleaning, it wasn't exactly right. Then I noticed that the cover plate was bent. The cover plate has a hole that the pivot point of the switch goes in. Mine did not go in and it just bowed the plate up, leaving the pivot pin loose on one end or maybe not loose but being mashed down. I miked the pin and gauged the hole with a drill bit. No way that pin was going in that hole. I put the cover in my vise and with the aid of two crecent wrenches staightened it and then drilled the hole bigger. I left .05 clearance and that feels about right. My bet is that the reason that the anchor end comes loose is that the cover plate did not support the other end. Anyway, that helped my swithc action a lot, it still ain't great, but is better.