Rule #1 - don't ever call it a "two stroke" tank ; )
You're in the UK I believe. Castrol GTX in engine and metering oil tank (under the seat). Check with some Brit owners, the original Castrol GTX does come under slightly different names in different countries.
In the US, too easy, they use GTX in the gearbox as well, not sure what they do in the UK.
There are other reasons why you'd use a lighter gearbox oil as well. One thing I didn't mention in a rundown of common problems was starter clutch issues. Pretty common.
If that's working for blokes in the UK, go ahead. Quite a few people around the world run straight gear oils successfully.
Personally, I would ignore anything you hear about alternate engine and metering tank oils though. GTX is what was recommended by Suzuki. It's been tested in the real world for decades. It's cheap as chips and readily available. I don't doubt that there may be better oils out there, but I'm not willing to risk my engine testing them when there's little advantage and no long term data.