Dear Arnold,
Interesting question, however I think your approach needs rethinking. The non-sequiter questions you list as examples are all simple objections and just becasue they are non-sequiters it doesn't follow that they are any trickier than any normal objection.
Perhaps you may have not identified that it is normal for these types of question to be asked if rapport and trust has broken down or not been established sufficiently in the preceding conversation.
"Are you deaf?" is a large concern as it indicates that the agent has not listened to what the respondee is saying, listening and responding is a significant factor in establishing any relationship.
Building rapport is one of the most significant factors in creating the conditions for a sale in the the UK (I can only talk about the UK). You could write a book on the Brits ability to be indirect, polite and not say what they mean! However the only way you will efficiently reach a mutually acceptable sale that will stick is by building rapport throughout the conversation.
I know that in other Western countires other qualities are significant - Italy - Knowledge, Spain - Efficiency (source Eurotelecultulture - pub Henley Research centre).
The bottom line here for Brits is work on building rapport, using empathy, honesty, not being pushy, good product knowledge, objection handling, listening etc etc etc..............
Hope this helps
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