Just kept an Ammyy scammer[*] on the phone for 30 mins. It was my civic duty. His faltering English meant most of my usual time-wasting techniques wouldn’t work. Here’s what I did in case you’ve got one on the phone right now and want some ideas (please add more in the comments):

• Keep thanking him for all the help he’s giving.
• Ask him to repeat every instruction at least 4 times.
• Crinkle crinkly stuff into the phone (I used tin foil). He phoned back twice to try to clear the bad line.
• If the conversation is stalling, walk into the bathroom and flush the toilet. I did this a few times, it confuses them enough you can steer the conversation to your own ends.
• Every time they mention a colour (“can you see the green box?”) explain at length how you are colourblind, and get them to describe other aspects of what they want you to click (forces them off script so buys you time).
• Reboot the computer at least twice (“yes, my computer is so slow and crashy, I’m so glad you’ve phoned to help me sort this out”). Each time I said I’d be back soon and went quiet for a bit.
• He asked me how many members of my family lived in the house (presumably for Ammyy licensing reasons), at this point I got into a several minute debate about whether my dog counted as part of the family.
• Near the end I just googled for horror sound effects and started playing them in the background.

Alas, he didn’t speak good enough English for me to use Counterscript, and it wasn’t quite appropriate anyway.

Any other keep-em-on-the-phone tips?

[*] Call from Indian-sounding call centre (1471 reveals nothing), saying he’s from Windows service centre, and errors have been spotted on my machine. He talked me through three steps: 1) Go to Application event log and showed there were “Errors” there. 2) Go to Run > cmd > assoc, and he read the unique-sounding code at the end of that command to prove he was from Windows (“only you and us know that code”). 3) Go to ammyy.com, where I was told to download their PC remote control programme. Not having a Windows box at home, it was a bit tricky to keep him going while he was talking me through the various dialog boxes, otherwise we could have gone on for hours.