Start the trace
When I get a call from any kind of scammer (tech support, double glazing, solar panels whatever), I use the same tactic. Partially cover the phone and move it about 18 inches away and then say to a non-existent colleague "I have another one, You start the trace and I'll keep them on the line".
I then go back and appear to be very interested. If they don't hang up quickly I do another bit with my "colleague".
Normally works well.