I don't think so..as long as nothing is touching.
There might be some connections that if lose, electricity will find a path to ground through a different circuit. when it happens usually it has to do with the turn signal and parking lights.
It looks like '62 one fuse is used for Dome & Brake lights.
Brake light switch closed power flows to the turn signal switch ===> Turn signal switch connections to the brake lights are normally closed ====>
Power flows to each tail light through seperate wires (through two connectors) ==> bulbs===>each has a ground wire in the trunk.
Maybe schematics help. These are based on my 67 so the connector cavity numbers and wire positions may be different.
Power flow when brake switch closed.
View attachment 1715348264
Power flow when Brake Switch Closed with Turn signal for left turn.
View attachment 1715348265
Dome Light
Power is always present at the dome light. The switches are in the ground wires. Any switch closed completes the circuit.
Based on that, here's how I interpret the '62 wiring diagram.
View attachment 1715348268
These wires from that fuse are always at system voltage.
In other words they are ready supply power.
View attachment 1715348274
Close any switch and current will flow through the lamp to ground.
View attachment 1715348278
Something has to be crossed for to connect the stop lamp wiring to the other stuff.
