I use my Master Appliance UT-100 butane iron, but any good iron or gun over 45 watts will do the job.
I use normal electrical 60/40 rosin core solder, and actually treat the connection like an electrical connection.
The music wire pushrods are coated and oily... they will not take solder as they are. I clean them up with emery paper... 400 grit sandpaper will work though.
After that, I slip the clevis on and give it a crimp with my Kleins (only to be sure it doesn't move while soldering). Like an electrical connection, heat one side and feed the solder in through the other. I like to put the tip of the iron on the wire, against the edge of the clevis, and feed the solder in through the end that attaches to the control horn.
I haven't had a failure in 15 years.
--- Rich