Would you give him the money back?

A buyer has put down 2000 euros for a car, I have turned down more than 5 interested parties and have probably wasted 5-6 hours of effort writing invoices, viewings and making phone calls.

after repeatedly came please don't sell it to someone else I want to buy it.

I prepared an invoice for him but he hadn't signed it yet. We agreed on the price for the vehicle. The deposit came 3-4 days later and then I waited at least 4 days until I got a reply as to when the remaining payment would be due and then he said yes, there were apparently problems registering the car with the other gentleman abroad, etc.) and I wanted my deposit back.

Should I return the deposit or not?

I read the following online:

A lawyer said that if the buyer has made a down payment, it's a declaration of intent and a purchase agreement has been concluded. Strictly speaking, I'm entitled to the down payment if the buyer backs out. Even if the purchase agreement has already been completed but not yet signed. The down payment is there to show that he intended to buy the car.