If you’re looking at having a shop perform work on your vehicle and they require a deposit up front, you should look elsewhere. If they need a deposit to begin work on your vehicle that means they do not have enough money to allocate labor or materials to your project, and will probably take your up-front deposit for other projects.
Shops that have a steady flow of business have a backlog of ongoing and completed work that contributes to liquidity and the ability to take on additional work without running dry. Most of these horror stories you see about enthusiasts dropping off their cars for upgrades or restorations always start with “I gave the guy a deposit and then he sat on the project”. That’s because the unscrupulous business owner took your money to pay other debts/go on vacation while you’re left with your [insert appendage here] in your hands. Stop giving these awful businesses your time and money.
ETA: To qualify this post, a 10% or some such deposit is not unreasonable to reserve your car’s space in the shop and to prove that you’re committed to getting the work done, and for certain parts that are a significant cost (superchargers, EFI systems) it would make sense, but if the shop cannot substantiate why they need a deposit or show you where the money is going to go then you are probably going to have issues.