For private sales, I can understand someone not wanting to pay a deposit but for private sellers and for us, if a deposit is not taken, the car is still for sale. Personally, I wouldn't pay a deposit on a private sale. If the car isn't right, there's a high chance you won't get it back unless you're a powerfully built company director with a can of red bull handy.
For private sales if a deposit is not taken, the first to pay the full amount wins.
It's easy to be lead up the garden path by someone if you're basing it all on trust but after you've been messed around, you learn. Keep taking calls / appointments etc but as long as you're straight with someone that someone is coming to view on X date and they very well may buy it. Sometimes people don't like that but if you're honest, it comes across like that and not someone trying to invent some superficial interest.
For us, if someone does place a deposit, handover/delivery is arranged at the same point. We will not hold a car indefinitely on a small deposit. Sometimes there are circumstances, someone has purchased but is off on holiday for two weeks, that's fine but I have seen people place large deposits on vehicles and then mentioned that they don't want the car for four months..
We take refundable deposits for distance customers who haven't seen the vehicle and can't get over for a few days. If the vehicle isn't what they thought, that's fine but we wouldn't put the vehicle through for preparation based on this.
VX's are a touch niche but I would suggest Tootle if you're looking to sell your car. Dealers bid for your car which keeps it simple and hassle free as the process can be.