I have a GiPro ATRE fitted and noticed that it was getting erratic showing 5th and 6th gear, often reading "0". The neutral light was also getting variable, and it was clear that the gear position switch was playing up. Ordered one from the US and replaced it and all was good again for over a year. (Item 40 below)
Since then it started playing up again, so I got some contact cleaner, removed the switch and sprayed it until it ran clear. Worked a treat, and I have fixed another one the other day. Definitely the preferred option in the first instance is cleaning it, although I have had to clean it more and more and decided to replace it.
The GSF1250 part is 37730-18H01 but I ordered number 37730-18H02, which is the later switch for the GSX1250FA with the identical engine. Works perfectly and I am hoping the different part number means Suzuki made it more reliable. I have not seen any GSX owners reporting issues
Regarding cleaning, Jools listed some helpful photos and is happy for me to link to them, so try this for a step by step if you need it:
Jools' post pictures are reproduced below with his consent:
1. Undo the red arrowed bolts
2. It will look like this. You can just see the gear position switch behind the gear shifter rod. You don't need to remove it - just use a long allen key or drive head. The sensor on the front just below the shifter rod with the single allen bolt is the speedo pickup (if your speedo is playing up, check that it isn't caked with old grease)
3. This next picture shows the switch up close. Undo both bolts and pull the switch gently back, being careful not to displace the o-ring
4. Flush the switch with contact cleaner until it runs clean, put blue loctite on the bolts and replace. Don't overtighten it.