Quoted from pins4u:Soldering is a skill just like driving a car, flying a 'plane or building a model boat.
It is something you need to learn. There are dozens of good tutorials on YouTube - I would start there.
I have seen people do an abysmal job using the most expensive equipment available and I have also seen perfect soldering with a $5 iron.
Whatever you buy it is not going to solder for you - YOU need to practice. Get hold of some junk electronics being thrown out like old stereos or cassette players and practice your soldering on that before moving up to anything else.
With all of that said, soldering a few wires to an EOS switch isn't exactly brain surgery BUT learning to solder might help you in many other ways.
FWIW, that Hakko with that tip would be perfect for the job you are suggesting as well as most pinball board work.
pins4u makes some excellent points. If you're lousy at soldering, you'll be lousy with a $200 iron as well as the $5 garage sale iron. I've been soldering for +40 years and I have no qualms using a $5 iron in a pinch and the joint will be just as good and clean as the $100 iron. Granted, a good temperature controlled iron with a good tip is definitely preferred for PWB work. I personally use some temperature controlled Weller's, but I bet those are +30 years old. When I eventually buy a new iron, it'll just be something that uses a temperature controlled tip that is common (i.e. not proprietary).
So this is what I would do: Get some decent 60/40 or 63/37 rosin core solder (i.e. has lead), flux (i.e. NOT plumber flux, it's acidic), some solderwick w/flux (all that stuff should be 'electronics safe') and grab some old stranded wire and go to town making slices and soldering/desoldering. Lead free solder will work, but it has a higher melting temperature, making it a harder to work with. Got a broken electronic gizmo setting on a shelf? Tear it apart and start to practice unsoldering and resoldering parts.
You'll be a pro in no time! When you're ready to move to SMD (surface mount), Amazon has some nice practice SMD boards for about $8ish.
Good luck and don't overthink it, it's not that hard.