where has anyone said not to rest between sets? Surely the very fact they've been referred to as sets means there must, by definition, be a rest period between them, otherwise it would just be constant exercise? I would say to try and limit your rest period - there are soo many people in my gym who do 1 minute weights, 5 mins faffing on phone, repeat for 3 sets = tying up a machine for nearly 20 minutes. If you are going to do this alternate with someone else, or arms/legs on different machines, or go at quiet times.
For OP - if there are multiples of the same machine empty, do not go on the one right next to someone else, leave a gap. aka the urinal rule. i.e. if someone is on treadmill 3, choose treadmill 1 or 5, not 2 or 4. Some people might complain about this 'I like the positioning of/view from this one' etc but it's weird, particularly in a gym where the machines are very crowded together, and, if you're a run-farter, very unpleasant for the person/people next to you. Obviously if it's busier it's fine.
Use the changing room to GET CHANGED and then LEAVE. People in mine spend ages just sitting there on their phones, which is disconcerting (never sure if they could be filming etc), I've stepped over people using it to stretch before, etc.
To be honest most gym etiquette is to just act like a normal person. Most people at the gym just want to do their own thing and ignore everyone else.