If you suddenly clam up when they get to a specific question, they're probably going to be able to guess the answer.
https://www.oyez.org/cases/2012/12-246
I don’t see how telling the officer you have $87k is probable cause for a search, anyway.
First, it is not illegal to have a car or cash.
Second, in the US at least the government does recognize a limited right to privacy in the form of the 4th amendment which spies to States as well. An officer cannot search you, your car or your home without a warrant from a judge or a tangible reason to believe you are committing a crime.
> The lesson here is clear: do not cooperate with the police
Suddenly clamming up is a problem, doing so less suddenly is not (I'm elsewhere in this thread roughly advocating for clamming up about anything not directly related to the traffic stop)