"To send somebody out in pursuit of some black chickpeas" is a Persian idiom that implies 'to make or ask someone to run an errand so that you be able to have/ buy some time in order to deal with your private affairs in their absence', like having or continuing a (secret) conversation with someone else.
According to its etymology, since 'black garbanzos/chickpeas' were rarely available in the markets, when someone wanted to buy them, they had to search many stores for a long time, and most of time they couldn't find them at all.
Today, its meaning has changed somehow, and it doesn't necessarily mean that we ask someone to run an impossible errand, but it means we use that errand as an excuse to send them away for a while just to have time to do something in their absence.
Suppose your classmate has come to your house and you are talking about some girly issues in the sitting room. Now you want to tell her a big secret about one of your classmates, but not in the presence of your younger sister who is sitting there too. So you ask her to go to the market and buy some snacks for you. In this way, you will have some time to continue your conversation until she is back. So you might say to your friend:
Well, I sent my sister out in pursuit of some black chickpeas. I'm sure that she won't be back for another 15 minutes, so we can talk more freely now."
And your sister, before leaving the house, might sarcastically say to you:
Okay, but I know this is just an excuse, and you are just sending me in pursuit of some black chickpeas!!! so don't think that you can fool me!
Is there any idiom, expression or proverb that conveys the same meaning or connotation in English (i.e. to make or ask someone to do an errand just in order to buy time so that you can deal with some of your private affairs)?
I have found to be/go on 'a wild-goose chase' but I'm not sure if I can use it or not.