What type of relay is the picture below? I am wanting to power some aux LED lights but would like the ability to switch them and have them come on with the high beams when they are switched off. I have seen a relay diagram on here that would work but I don't know how to find it.
What you have in the diagram is a conventional SPDT relay wired in a unique and effective isolating circuit. The 2 inputs can never accidentally cross-connect due to non-bridging contacts in the relay. I do a lot of relay logic circuits, from auto to HVAC to communications. I really like this circuit. Don't forget to use an inline fuse for the lights.
The relay shown in the diagram is a standard automotive relay, but that's not how you should wire up auxiliary driving lights.
A search for "automotive relay" will bring up the kind you need - available from most automotive suppliers, so find one in your location. They have four or five pins, numbered 30, 85, 86, 87 and 87a. The coil is across 85 and 86, and the contacts 30 and 87 (87a, if present, is the 'normally closed' contact).
Connect it as follows: 85 to ground. 86 to a switch, then to the feed from your high beams. 30 to the battery (via a fuse), 87 to the lights, then to ground.
This will then mean that when the high beams are on, AND the switch is closed, the coil will energise, closing the contacts and switching on the lights.