Sounds like you have a bad wire somewhere.
I'd have someone sit on the mower, (better yet by pass the seat safety switch) and then get it to act up
pulling the arms in. Follow the wires, especially from the side that was the worst, and poke about with a screwdriver (or such) trying to get it to work properly.
Also, I've gotten MANY switches, with bad / poor contacts inside to function (like new),
with just a couple of squirts of Liquid Wrench. It helps remove any build up /contaminants, etc.
Also, just because the part is new, doesn't mean it's good. So keep that in mind.
I'd also un-plug, inspect / clean
any/all connectors you can find.
After cleaning, some Di-electric grease will keep moisture out and the
connector working as it should..
BTW, I have the exact same mower, (2005 model with a Briggs)