That’s a developed country view to assume people are queueing up in their vehicles.

People in developing countries just hand carry a tank.

Mostly it's TukTuk drivers who simply switch off their engine, and simply push their vehicle when it's time to move up.

A quick scour of Google seems to come up with about 0.2 gallons per hour (about 900ml) for an idling engine, so assuming you keep your engine running (and discounting extra fuel used moving forward in the line), let's say you have a 16 gallon tank, you'll be able to run the engine for about 80 hours before stalling. Plus or minus 20% bearing in mind size of engine, tank size, ratio of time spent idle vs. moving, how much fuel you start with (you wouldn't be at a fuel station with a full tank, I'd imagine?)

80 hours is a lot less than I thought it would be.

Would be a function of how long the line is not how long you have to wait since presumably the people in line aren't needlessly wasting gas while not moving.

They probably turn off their engines when queued.

So, infinite.