Put the OEM solenoid back in the bike and see if you can get your 12 bucks back from Amazon. I'm glad I was wrong about what your problem turned out to be but I still stand by my opinion of Amazon el cheapo automotive/motorcycle replacement parts.

It's a shame that the OEM stuff has become so obscenly expensive but that's only going to get worse since our bikes were discontinued by Suzuki 7 or 8 years ago.

I remember looking at Partzilla for the price of an ignition module for a savage a few years ago (Suzuki calls it an igniter) when someone on here was looking for one. I was astonished at the time that the price was just under $300 for what is basically just a circuit board with a transistor and a handful of resistors and capacitors soldered on it. I remember thinking "Holy Sh*t ! I hope nothing happens to the one in my bike."

I looked today and that part is now $827 !

On second thought maybe you ought to keep the Amazon solenoid for a spare just in in case...