connecting cigarette light socket to aux battery on 2013 plug-in hybrid prius

First, you do NOT want a "trickle charger".
You need a smart, automatic, tender type battery charger.

When you buy one, it should come with an SAE battery cable that you can attach directly to the battery
and then plug the tender into that.

 

or just connect it to the jump point under the hood. i just picked up this one:

ref=sr_1_1_sspa

 

Presuming you want this cig lighter socket in the dash somewhere? You'd need to tap-in the positive (likely red) wire of the cig lighter to a constant-on 12 volt wire; one such wire runs to the OBD port. It'll "probably" be this:





You could verify which it is with a test light.

Then connect cig lighter negative (likely black) wire to bare metal of the car body, say clamped under a bolt or nut head.

That said, cigarette light connecte chargers are pretty old-school, not practical with modern cars that have existing cig lighter sockets that are not constant-on. You have this charger already?

FWIW, I'm using a CTEK 4.3 charger (rebadged now as CTEK 5 IIRC), and have wired the quick-connect wire harness that came with the charger, at the 12 volt lead-in at the underhood fuse box. Access to that 12 volt point is shown in the @NutzAboutBolts video:

^ He makes it look easy, but be prepared to spend about 10 minutes at this, lol.