It's normal to see 12v on both sides of the solenoid. The solenoid internal circuitry is very low resistance, so if you pick either leg and reference it to ground, you'll get the same voltage reading.
I'd still replace the solenoid first or at least grab one to keep as a spare. If you have the Ace Maxxam 2R, I believe they use a non-standard 2-pin connector. Upload a pic of your solenoid connector if you'd like me to confirm.
GY6 Starter Solenoid Relay
https://www.buggydepot.com/product/142/ ... relay.html
Other causes would be the switch, or wiring in between.
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