terminology is often misused.
When the term short is used to me it means that a wire is unintentionally connected to ground because of a failure of insulation (or perhaps to another wire for the same reason).
A short to ground causes fuses to blow and wires to overheat and insulation melt due to the heat.
A wire that is open means that current is not being passed to the load and basically nothing happens.
I think you have an open circuit (noting not blowing fuses and no smoke from burning insulation).
I see in the pictures that you have the Scotch lock connectors that are not noted for extreme reliability.
When measuring for "shorts" with a meter a light
bulb will read very close to "0" ohms as the filament is basically one of those shorts that gets hot and glows.
The filament heats up and the resistance increases dramatically and thus does not draw excessive current after a quick surge to heat things up.
I would look at any of the Scotch Lock connectors I could get to and sharpen the probe on your meter to penetrate the insulation or better still perhaps just use a straight pin to do it and probe to the copper conductor as you work your way back.
Since one of the bulbs works and they share a common ground the problem is probably not in that part of the circuit.
A wire is not likely to have separated within it's insulation, but it is possible.
Most likely are those pesky splices between the connector and the bulb.
Use the pin and meter with the wire energized and find out where you have the interruption.
Step by step wins the day.
Find any place you can get to the wire and poke that pin in to check for voltage.
I would not worry particularly about the pinprick through the insulation.
The first place to check is right before the wire goes to the socket as often these taillight sockets are (Redacted) up.