I'm installing a stereo head unit and don't have sound. This blue wire comes from the included harness and is the amp control wire. The control wire on the other connector at the unit also says amp control and isn't connected to anything. I'm assuming I have to connect the two wires and this thing (plus heat shrink wrap...?) will help. I'm unsure if I should use this or cut and strip the wires and find some wire nuts. How do I use this connector, (if it even is one)?
The point that I'm making is that catching fire, even in these circumstances, is extremely unlikely, especially with a somewhat modern head unit. Even going right off the positive terminal (shudder), it's much more likely to brick the deck in a way that no longer conducts electricity than it is to conduct AND resist enough to start a fire and/or dump a significant amount of current from the battery. Electrical safety and best practices are definitely important though. (OP please do not do the things that this commenter listed)
That's fair. My assumption, however, is that OP is trying to identify the connector to figure out how to properly use it. I couldn't have told you the name of the connector a couple of days ago and I've done a fair amount of PCB design, a bit of basic mains wiring, and just completely rewired my guitar. I DID know the name at one point but forgot it. I think it may have been more helpful, from your side to raise you very valid concerns to OP in a manner that offered them constructive avenues to learn further and not do horrifying things with their car electrical systems.
Seriously, thank you for speaking up on those horror shows that you've seen. I hope OP takes note and learns to do it right.