I think the closest you will get is to make use of autocorrect to turn this behaviour on. I would then use a keyboard shortcut to turn it off again. I am assuming that 'inQuotes' is a character style and that your quotes are always shown inside double quotes.

In a document type a double quote, select it and apply the inQuotes character style. While it is still selected, go to File>Options>Proofing>AutoCorrect Options...>AutoCorrect. In the Replace text as you type section put "[[" in the Replace field and select the Formatted text option and click OK

This will add an autocorrect function that converts [[ to a " and turns on the character style. Then as you finish your quote you can press Ctrl-Spacebar to turn off the character style again.

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Andrew Lockton
Chrysalis Design, Melbourne Australia