I had trouble finding the "Apply for the 90-day report". I could not find the button on the MFA website. Eventually found it elsewhere.
tm47.immigration.go.th
All plain sailing after logging on. I filled in the requested information, submitted the form, "SUCCESS" flashed up on the screen, and a completed TM47 appeared (as shown by
@Yorky). I have checked my emails and found an automatic response from Immigration, with a copy of my application to extend my 90 days in Kingdom. I guess I now sit back and wait for the email confirming the extension. Print and attach to the passport.
P.S. How long has the online system been in place? I have tried previously hundreds of times to report online without success. This is the first time I have successfully applied online. Well done Immigration, we eventually got there! The new system works, fingers crossed.