I've seen on here where someone paid in full, then the seller backed out saying something about he promised his cousin or some BS. I'm guessing he was offered more $$ and decided to be a dick to the first buyer.
No matter if you pay a deposit, pay the asking price in full up front, or pay nothing at all until delivery, have the seller (and yourself) sign a bill of sale. That way, you have a legal claim to the firearm if they try to squirrel out of it. The bill of sale should have all the info you need about the firearm and seller's name (HPD requires the seller's name). Make sure you include a clause that cancels the sale if your permit application is denied, like "contingent upon permit approval".
If you're sincere enough to apply for the permit, most sellers are cool with holding the pistol those 2 weeks without any deposit. I always call, text or email the seller the day I apply so they know when to expect the permit to be ready.
Having the deal in writing from the start can go a long way toward avoiding problems and miscommunications. Anything you feel is important to the deal, just add it to the paper so you both agree to it. Nothing complicated.