First off, have you physically cycled the trim servo while on the ground? If it’s moving correctly full cycle in both directions, then it’s the trim indicator or connection. If it’s not moving correctly, then it’s off to the troubleshooting races.
If it is corrosion, any good contact cleaner will do the job. They sell CRC Contact Cleaner at AutoZone if you have one near you, or Walmart for that matter.
The thing is, if the issue really is corrosion, you want to prevent it from happening again, so when you reassemble it (or any electrical connection/connector plug for that matter), fill the female plug with a silicon dielectric insulating compound; it will protect and lubricate the contacts and prevent water and oxygen intrusion to the contacts mitigating further corrosion. I recommend Dow Corning DC-4, which has been an a great product for many years. You can buy it off of Amazon and 5 oz tube will be lifetime supply for most folks. The good news is that the shelf life is about that too. As a bonus, it’s a perfect rubber protectant as well; useful for wiping down all of your rubber seals (car doors...) and installing o-rings as well.
While the tail-cone connector is an easy place to start, don’t forget to check connections all the way to the switch and indicator. The simple action of disconnecting, spraying with contact cleaner, applying DC-4 and reinstalling at all points might solve it and is good preventive maintenance too.
Molex style connectors work well, but a little corrosion protection never hurts. If redoing the connector at the trim servo doesn’t do the job, then you need to start basic electrical troubleshooting, which is bisecting the circuit, test connections and components, eliminating the good ones until you find the fault.
The most likely fault is the connections of the circuit or the trim switch, keeping in mind that whatever gets used the most, wears the most. If those prove out, then just keep testing and eliminating the good components from the puzzle. Happy hunting.