Straplight

The Straplight solves one specific problem: every other light in DOORS occupies your hand. This one is strapped to the head, so you can keep a key, a lockpick or a bandage equipped and still see. It is classified as a Directional Light Source and a Dependent Item.

In The Mines, Jeff sells it for 150 Gold, and the Pre-Run Shop asks 100 Knobs for it; it also shows up in Mines containers. The shop blurb sums it up as hands-free light.

Fuel

The wiki lists 2 minutes of fuel, split into two bars of 1 minute each, and a single battery is enough to refill it completely. That pairs it with the Battery Pack, which stores up to four batteries for later recharges.

Louie trades

Handing a Straplight to Louie gives a 20% chance that he returns a Battery Pack or a Bandage Pack, the same odds he applies to a Flashlight, Vitamins or Lockpicks, so it is rarely worth giving away unless you already carry a spare light.

Because it never takes over your hands, it is the natural pick for runs that rely on lockpicks, shears or healing items rather than on a held light.