Reliable parts supplier? Hitchcock's has everything you need, generally only 2-5 days to your door, depending on where on this planet you live. They also have downloadable manuals, tools, bling, etc. The amazing part to me is the thoroughness of the website and the availability of solid, experienced, real-human assistance.
https://accessories.hitchcocksmotorcycles.com/31288?qty=1&continue_url=https%3A%2F%2Fwww.hitchcocksmotorcycles.com%2Fpartsbook-pages%2F4096PART No. 585632; REGULATOR/RECTIFIER UNIT 3 PHASE (GT) with a 3 pin connector and a 2 pin connector; £70.00
There's no info on the year of your GT535 in your post, always helpful.
Do you have a VOM meter? How old is your battery? What happens to the battery voltage when the starter is operating? Down to 9V? Have you checked the ground cable attachment at both ends to verify there's actually a low resistance connection? Corrosion or a layer of paint will stop 12V cold.
As Derottone pointed out, the
battery starts the bike. The Reg/Rec keeps the battery topped up and doesn't cook it whilst recharging. If you have a fully recharged battery,
in good condition, the voltage should reliably be
at least 10.5V - 11.5V while the starter is operating, going back to 13.5V - 15V once the bike starts. If you aren't seeing good voltage
after the engine is running,
then the Reg/Rec is suspect, but that won't stop the machine from starting.
If the battery is "tired" and has built up internal resistance thru chemical aging, it simply cannot deliver the necessary current. A new Reg/Rec won't solve that. A new battery can work wonders.
Get your VOM out, do some investigating, write down the results. Help us help you.