The “hang” in “hang fire” is the English common verb “to hang,” meaning “to suspend” in a variety of senses, used here in a figurative sense of “to hold in a state of inaction,” the same sense we use in the phrase “hung jury,” meaning a jury unable to reach a verdict. “Hang fire” can also mean “to delay something that was expected to happen,” since a gun like a blunderbuss or a musket that “hangs fire” may fire on its own in a moment or two (making such weapons inherently dangerous to use).
Unlike so many expressions, this one is well understood. It dates from a time when firearms were loaded using a gunpowder charge poured from a flask, which was then ignited by a spark from a flint striking against an iron plate. Gunpowder was notoriously unreliable, partly because it varied a great deal in quality, but also because the slightest damp stopped it igniting properly. When this happened, the powder in the firearm smouldered instead of exploding and was said to hang fire. (This was highly dangerous, as you may imagine because the remainder of the powder might explode at any time, perhaps while its owner was trying to clean the gun out and reload it.) So to hang fire became an expression for some event that was slow in acting or of a person hesitating, usually with the inference that a matter of some importance was involved.
“Flash in the pan”
This expression should not be confused with a closely-related one a flash in the pan, for an ineffective effort or outburst. This referred to gunpowder that burned fiercely but ineffectually in the touch hole of a gun, without igniting the main charge.The powder in the “pan” of a flintlock firearm “flashes” just fine, but the main charge fails to ignite. “Flash in the pan” has been used figuratively since the late 17th century to mean something that attracts great public notice but has no lasting effect or success (“These were flash-in-the-pan early Nineties pop stars who combined European dance music with tints of R&B and afro-Caribbean pop,” 2011). Unlike something that “hangs fire,” a “flash in the pan” attracts attention at least at the outset, even if it turns out to be, in the lingo of the recording industry, a “one-hit wonder.”